From a continuum mechanics standpoint, I don't believe that there is any difference in the mathematical formulation. The term "creep' is sometimes used in viscoelastic materials to characterize the viscous part of the material model. In some finite element packages (such as Abaqus), it is the only way to define a viscoelastic material that doesn't have a long term elastic component.
In metals (even ones often characterized as elastic or elastic plastic), they often suffer from slow, rate dependent deformation at stresses that are far below the yield stress when subjected to continuous stress. This issue is exacerbated at higher temperatures.
In ordinary materials, e.g metals, the number of vacancies (namely empty lattice sites) increases exponentially with temperature. Creep is dominated by "dislocation climbing". The creep rate can by described by an Arrhenius equation.
In amorphous polymers creep occurs by "macromolecules sliding" . The creep rate depends on the retardation time spectrum and involves comples , non-equilibrium, analytical treatments, To this end please see the following papers:
GRASSIA L., D'AMORE A. (2006). Costitutive law describing the phenomenology of subyield mechanically stimulated glasses. PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS, vol. 74, p. 21504, ISSN: 1539-3755
GRASSIA L., D'AMORE A. (2009). The Relative Placement of Linear Viscoelastic Functions in Amorphous Glassy Polymers.. JOURNAL OF RHEOLOGY, vol. 53, p. 339-356, ISSN: 0148-6055, doi: 10.1122/1.3056631
Although the same name is used, both phenomena are not equivalent. In fact the name creep comes from the creep test, in which a sample is submitted to a constant stress state and the time-dependent deformation is registered. You may want to investigate the phenomena, for example, by setting a constant strain state and registering the time-dependent stress, this leads to the stress relaxation test.
Viscoelastic materials present a time-dependent reversible stress-strain behavior. You apply a constant stress, the material slowly deforms, you remove the stress, the material slowly returns to the original form (if you have access to a leather couch, you may observe this phenomenon in first-hand) . In order to do so, the material has to keep a memory of the original form. Polymers have physical crosslink points or mechanical entanglement points which gives the material this reference to the original form.
Creep in metals is caused by the irreversible movement of either vacancies, or dislocations, or grain boundaries and none of these movements keep track of the original position, so, creep deformation in metals shows a time-dependent stress-strain deformation behavior, but this time the material does not return to the original form as the stress is removed. We call this behavior viscoplastic .
In summary, the name creep is used for both phenomena because they refer to the same kind of mechanical test, but they refer to different phenomena.
In fact almot all materails creep. A solid material forgets that it was once a liquid ! If you look at glass panels in old cathedralas, you find them creeping under their weight near the bottom edges.
This is a really common mistake. You're definitely right that glass panels creep over time. However, The idea that old windows are thicker at the bottom than at the top due to creep is not true. The relaxation time constants in glass are far too long for that kind of creep to occur over 100's of years. If that were the case, then glass under bending loads should creep far faster and telescope lenses would need to be readjusted or replaced constantly (since telescope lenses need to be made very precisely.)
The reason that old glass windows are often thicker at one end than the other is due to the manufacturing processes used at the time. They had a very difficult time consistently making large panels of very flat glass.
I've attached two papers. One attempts to calculate the relaxation times theoretically and found that they were probably closer to billions of years than hundreds of years. The other looked at glass plates over 30 years and and measured the deformations experimentally. They found deformations on the order of nanometers.
Creep of certain low melting point materials /alloys like Pb or lead-tin alloys, wax candles etc. can take place at room temperature.Glass may not be a candidate material for RT creep. Creep mechanisms may be different for metals and visco-elastic materials,polymers etc.Creep otherwise is in general observed in all materials.
I agree with Claudio. Basically, visco-elastic and visco-plastic phenomena are the consequence of very different things occurring at the micro-scale. Macroscopically, you would observe that visco-elastic strains are reversible, whereas visco-plastic strains are permanent, given that they are related to (mainly) dislocation movement.
Finally, in metals subjected viscous behaviour, you could have both visco-elastic and visco-plastic strains. The latest is dominant under significant stress levels.
Metals are viscoplastic. They show rate dependence after the yield whose value may also depend on rate of loading. There is no yield for pure viscoelastic material.