When you look at the references cited in a particular article, you are looking back in time. All cited articles were, necessarily, published before the current article.
When you look for articles that cite the article you have, you are looking forward in time. All citing articles were, necessarily published after the current article.
If an article is relevant to your topic, you want to look at the research it cited (backward citation). But it can also be very helpful to see who has cited it (forward citation). There are several different ways to do this, and the results will overlap -- no single method is comprehensive.
Google Scholar provides forward citations for some articles. It has a broader range of documents included (not just peer reviewed journals, but reports, pre-prints, etc.) and doesn't eliminate self citation or de-duplicate the results.
Web of Science is a vast, multidisciplinary database, which includes the Social Science Citation Index. This index allows you to do a "Cited Reference" search if you select that tab. This will retrieve other articles (from a prestigious list of peer reviewed journals) which have cited the target article, and it also shows the references for the the original article... both forward and backward citation.