The shifting balance theory (which traces its origins back to Sewall Wright  in 1932) is deeply rooted in the idea of fitness landscapes. It is a mechanism that explains how populations can shift their position to new adaptive peaks via subpopulations that find themselves in adaptive valleys and reach other peaks (both in the original formulation through genetic drift and natural selection). When the subpopulation found a new peak it might expand its range and pass on the new traits to the rest of the population.

A possible point of critique is that the simplest depiction of the theory (with adjacent fitness peaks) ignores constraints that might change the evolutionary trajectory and that will change the path in the fitness landscape from a straight line to a curve.

(Two interesting papers about this direction of thought are Arnold 1992, and Futuyma 2010)

The punctuated equilibrium is based on the observation that taxa are conservative and remain at an equilibrium state that marks a morphological and ecological stasis (although some formulations still allow for shifts to take place). Changes seem to occur less in a gradual manner and more punctuated in relatively short time intervals. The basic point of interest for this is the species level.

The idea of the punctuated equilibrium is not wedded to any specific mechanism. And Niles Eldrege and Stephen J. Gould (who originated the term in 1971 (conference talk)/1972 (paper publication)) modified the mechanism involved several times, for example moving away from the idea of allopatry as the “standard” agent of reproductive isolation.

I hope this helps a bit to see differences (and similarities).

Arguments have been made linking shifting balance theory to punctuated equilibrium theory in the the following fashion: if the transition from one peak to an adjacent peak is going to take place at all, it is most likely to occur quickly, and as a result the transition will be fast and appear punctuated in the fossil record.

The answers before were certainly correct. However, I am reluctant to call Punctuated Equilibrium a theory, because the fossil record does not really permit a test in most cases. The reason is that we would need a case in which (1) continuous sedimentation had occurred over longer geological times, (2) a dense sampling over the preserved rock sequence (=many time slices), (3) a large sample for each time slice that plausibly forms a population (and not a time-averaged sample), and (4) the sampling should cover large geographical areas to ensure that changes in a large population are identified. This is very, very rare to find. As for the palaeogeographical aspect, almost impossible. Hence, true punctuations in evolutionary lineages will be very hard to distinguish from simple gaps in the fossil record, or the immigration of a closely related taxon that might have evolved gradually from a neighbouring population - phenomena that are abundant.

This does not mean that we shouldn't think of punctuated equilibrium as an interesting alternative to other modes of evolution. We just cannot expect to be able to test all possible hypotheses in palaeontology. Very unfortunately so.

Genetic drift means shifting balance theory as well Wright’s rule and Wright’s rule means the punctuated equilibrium theory

a) Genetic drift means shifting balance theory

In 1982, Wright wrote and article entitled ‘the shifting balance theory and macroevolution” and noted that: The local sampling event or other form of random drift, and local occurrences of the drastic mutation, may thus be intermediary precipitating cues, but these will be of no avail without the vacant niche. The latter will usually be effective in inducing a macroevolutionary step even though the exact time and place of its first establishment depend on the former (Wright, 1982).   ii) The most likely precipitating cause of the origin of a macroevolutionary step is thus presentation of a vacant ecological niche to a species with a population structure that is favorable both for incipient speciation and for operation of the shifting balance process (Wright, 1982).  In addition, the shifting balance theory is based on the role of genetic drift (Wolfe, 1983). The genetic drift plays a crucial role in the shifting balance theory (Gardner, 1991).

So, it is proved that genetic drift means the shifting balance theory.

b) Genetic drift means Wright’s rule, Wright rule means the punctuated equilibrium theory

Genetic drift means Wright’s rule, Wright rule means the punctuated equilibrium theory and the documents are place here:

Gould and Eldredge used “Wright rule” instead of genetic drift as well as the shifting balance theory and its evidence is that they argued: “we choose Wright's name for our designation because he (1967, p. 121) explicitly suggested that speciation might by truly stochastic with respect to the direction of evolutionary trends” (Gould and Eldredge, 1977).

In addition, the following the documents are also proved that Gould and Eldredge used “Wright rule” instead of genetic drift as well as the shifting balance theory:

Wright exploited random drifting four times (Wright, 1931) and seven times (Wright, 1982) for rapid evolution of new species in populations. For example, i) The size of population is sufficient to prevent random fixation of genes, but insufficient to prevent random drifting of gene frequencies about their mean values, as determined by selection and mutation (Wright, 1931). ii)  Random drift from causes other than accidents of sampling (referred to in 1931) was treated mathematically in 1948. The last phase of the shifting balance process, the spreading of a favorable interaction system from its center of origin throughout the whole species by excess proliferation and dispersion, still waits for full mathematical treatment (Wright, 1982).

Similarly, Eldredge and Gould also exploited genetic drift/drift four times (Gould and Eldredge, 1977) and five times (Gould 1980) for macroevolution of new species in small and isolated populations. For examples (in Eldredge and Gould’s words): i)  In fact, it is so weak that the change could easily be accomplished by genetic drift, even in large populations (the smallest population size for which such change could occur by drift at least 5% of the time is only 10,000) (Gould and Eldredge,1977). ii) Evolutionary biologists must now take seriously the proposition that many, if not most, changes in structural genes drift to fixation in the neutral mode, do not affect phenotypes, and are therefore both irrelevant and invisible to Darwinian processes (Gould and Eldredge,1977). iii) Although aided by founder effects and even (possibly) by drift, although dependent upon isolation from gene flow, although proceeding more rapidly than local differentiation within large populations, successful speciation is still a cumulative and sequential process powered by selection through large number of generations. It is, if you will, Darwinism a little faster (Gould, 1980).

In 1931, Wright exploited isolation thirteen times and small population fourteen times (Wright, 1931), in 1982, Wright exploited small/small colonies/small change ten times for the macroevolution of new species in small and isolated populations through genetic drift. For examples (in Wright’s words): i) The effect of small size of the subgroups in bringing about random deviation in this and other cases is not here considered (Wright, 1931). ii) Complete separation of the species into large subspecies should be followed by rather slow and more or less closely parallel evolutions, if the conditions are similar, or by adaptive radiation, under diverse conditions, while isolation of smaller groups would be followed by a relatively rapid but more largely nonadaptive radiation (Wright, 1931).

Similarly, in 1977, Eldredge and Gould also exploited small population three times, small twenty two times, isolation seven times and isolate fourteen times (Eldredge and Gould, 1977). In 1980, Gould exploited small eleven times and isolation thirteen times (Gould 1980) for macroevolution of new species in small and isolated populations. For examples (in Eldredge and Gould’s words): i) Small numbers and rapid evolution virtually preclude the preservation of speciation events in the fossil record; in any case, speciation does not occur in local sections inhabited by abundant ancestors (Gould and Eldredge, 1977). ii) It emphasized the crucial role of isolation from gene flow and did promote the importance of small founding populations and relatively rapid rates of change. Thus, the small peripheral isolate, rather than the large local population in persistent contact with other conspecifics, became the incipient species (Gould 1980).

Furthermore, Eldredge and Gould exploited “Wright’s rule” ten times (Gould and, Eldredge, 1977) and “Wright” ten times (Gould, 1980) as the mechanism of macroevolution in small and isolated population through the punctuated equilibrium theory. i) All movement from the micro to macroevolution must be translated through the level of species by Wright's grand analogy, not merely extrapolated up in continuity (Eldredge and Gould, 1977). ii) We suggest that the "Speciation theory of macroevolution" can be explored by working through the details of Wright's grand analogy and considering the consequences (Gould and Eldredge, 1977). iii)  Wright's rule also requires that speciation be common in order to provide enough raw materials for species selection (Gould and Eldredge, 1977). iv) We suggest that this proposition be termed "Wright's rule," and that its testing be an item of high priority in paleobiology. v) Macroevolution and the Wright Break (Gould, 1980). vi) What we call "anagenesis," and often attempt to delineate as a separate phyletic process leading to "progress," is just accumulated cladogenesis filtered through the directing force of species selection-Wright's higher level analog of natural selection (Gould, 1980).

So, it is clear that genetic drift means Wright’s rule, Wright rule means the punctuated equilibrium theory.