Both platforms use different sets of full texts of publications and different algorithms to automatically search for citations. Very often GS finds more citations than RG, but not always. There is no connection between the platforms to exchange citations. This is a frequently asked question here, see these discussions (just a selection):

https://www.researchgate.net/post/In_Google_Scholar_my_master_thesis_got_a_citing_but_in_Researchgate_that_does_not_visible_Why_does_it_happen/1

https://www.researchgate.net/post/Can_someone_help_me_understand_why_there_a_difference_in_the_number_of_citations_shown_in_a_persons_Researchgate_and_Google_Scholar_account/1

https://www.researchgate.net/post/Why_is_citation_count_of_research_articles_different_in_Research_gate_from_that_of_google_scholar/1

https://www.researchgate.net/post/Why-does-my-article-citations-appear-in-google-scholar-but-not-included-in-research-gate/1

https://www.researchgate.net/post/Why-some-citations-are-not-recorded-which-are-found-in-google-scholar/1

https://www.researchgate.net/post/Which_is_more_accurate_in_reflecting_research_outputs_Google_Scholar_or_ResearchGate2/1

https://www.researchgate.net/post/Does_anybody_know_how_we_can_add_the_missing_citations_in_Research_Gate_as_will_as_Google_Scholar_profile/1

https://www.researchgate.net/post/Does_anyone_know_how_long_it_takes_for_Google_Scholar_to_pick_up_new_citations_from_ResearchGate/1

https://www.researchgate.net/post/Recent_publications_and_Citations_on_ResearchGate_are_not_getting_indexed_in_Google_Scholar/1

https://www.researchgate.net/post/Is_there_any_method_to_add_missing_citation_of_your_work_in_RG_As_most_of_the_papers_have_more_citations_as_per_google_scholer_but_very_low_in_RG/1

https://www.researchgate.net/post/How_to_include_all_citations_on_RG_and_Google_scholar_citing_your_manuscript/1

https://www.researchgate.net/post/How_can_we_add_citations_in_google_scholar_and_Research_Gate_for_our_articles/1

https://www.researchgate.net/post/How_can_I_link_my_articles_on_research_gate_to_google_scholar/1

https://www.researchgate.net/post/How_to_link_Research_Gate_article_citations_to_Google_Scholar_and_vice-versa/1

https://www.researchgate.net/post/I_have_4_citations_in_Google_scholar_can_these_citations_be_captured_by_RG/1

https://www.researchgate.net/post/How_to_add_missing_citations_on_Google_scholar_Research_gate_and_Scopus/1

https://www.researchgate.net/post/Does_any_know_how_can_I_add_missing_citations_to_google_scholar_and_resaerch_gate/1