This might partly depend on the area you are working in. In my field, social psychology, there currently is an active debate on issues of replicability, including the merits of "direct" replications. Interestingly, it may not be so easy to determine whether a direct replication (i.e. following exactly identical procedures) captures the same hypothetical constructs as the original study it aims to repeat.

For a more extended discussion, see

Stroebe, W., & Strack, F. (2014). The alleged crisis and the illusion of exact replication. Perspectives on Psychological Science, 9, 59-71. doi:10.1177/1745691613514450

In the software engineering field as well, replication is an emergent issue with an active debate. I am unaware of any usage of the terms "close, strict and literal", as the term used in SE is "exact replication" for "one in which the procedures of an experiment are followed as closely as possible to determine whether the same results can be obtained" (Shull et al. 2008), while conceptual replications for "one in which the same research question or hypothesis is evaluated by using a different experimental procedure"; the term "non-exact replication" is also used for the latter (Juristo et al. 20111). See also the special issue by Carver et al. 2014.

Shull, F., Carver, J., Vegas, S., & Juristo, N. 2008. The role of replications in Empirical Software Engineering. Empirical Software Engineering, 13(2): 211–218.

Juristo, N., & Vegas, S. 2011. The role of non-exact replications in software engineering experiments. Empirical Software Engineering, 16(3): 295–324.

Carver, J. C., Juristo, N., Baldassarre, M. T., & Vegas, S. 2014. Replications of software engineering experiments. Empirical Software Engineering, 19(2): 267–276.

Hello Sheikh Umar,

The connotation is the same, to have a replication which resemble as much as possible to the baseline experiment. I prefer to call it a literal replication.

kinds,