Why would you expect them to remain the same? They are two different platforms. Papers captured in Google Scholar may not be on ResearchGate, especially if the authors are not on ResearchGate, hence it is expected that a particular authors' citation indices may be higher in Google Scholar, when compared with ResearchGate.
Prof., that's not a good answer. All papers are immediately published by Google Scholar as well as by the research gate. Alternatively, a researcher can add directly, either automatically or manually. I have the same paper in both and the same citation. Why the changes?
Johnson O. Esua already made the most valid point here. RG does not include all citing papers in its database since its algorithm only scans through a selection of publishers while Google Scholar just gives you everything that looks sort of scientific and isn't blacklisted.
For that reason, your Google Scholar metrics will usually be higher than your RG metrics (which in turn are higher than actually rigorous assemblies like Scopus or Web of Science). For that reason, always cite the source of your metrics; I wouldn't recommend the RG ones, though.