This is an excellent question that illuminates the variations of terminology and conventions across all the disciplines that use (rely on) statistics. The answer I share here is my experience and opinion...though I believe it is pedagogically and pragmatically sound.
To answer the question asked at the end of the original post: Yes, the terms may be treated synonymously...however they may be used contextually to highlight two potential differences in the data collection protocol or the samples obtained. The first difference is to distinguish if the “waves” were collected at the same time or not. The second difference is to distinguish if there is any chance of “overlap” between the samples. While I personally would be inclined to use “pooled” for the first distinction (the data collection protocols were pooled in that they occurred at the same time), whereas I would be inclined to use “repeated” for the second distinction (allowing for the fact that some individuals may appear in more than one of the cross-sections). However, it appears the author of the first reference cited in the original post would use pooled for the second of my situations.
To elaborate slightly, I will reference an experimental design I unpack in some detail with my students...the posttest-only design using an "independent" pretest sample (see Shadish, Cook & Campbell, 2002, p.117). In brief, the experimental design is two pre-existing groups where one group receives a treatment (and the other is the control). When pretesting is not possible, this design proposes sampling different subsets from the groups for a pretest measure. The key point is that it is not uncommon for this design to have data collected in such a manner that it is not possible to determine if any of the pretest participants also appeared in the posttest groups. In this context, I would be more inclined to say this design is an example of a repeated cross-section design instead of a pooled cross-section design.
Happy to elaborate more if possible.