A citation in a publication is referring to another publication (called a reference), which has to be listed at the end of the text or in a footnote. A mention is not necessarily a citation, but a researcher can also be mentioned in the acknowledgements or elsewhere. However, it seems to me that mentions are often not clearly distinguished from citations.
In addition to the comment by Wolfgang R. Dick , I note there are some mentions on social media (such as if I have an article discussed on Twitter) which count towards your statistics. That is usually summarised on my profile page in RG as well.
Per general understanding both are same. Specifically
Citation is more academic. It refers to referencing a source of information. Mention is typically a generic term. This applies to anyone referring to someone or something.
I have to contradict to Atul Kumar Kuthiala , citations and mentions are not the same, depending on the scientific field. In natural sciences where the majority of publications happen in journal papers, one can consider identical. This way only citations are registered and summarized in scientometric assessments.
However, in social sciences and humanities, where the more typical form of publication is proceedings, monographies and other type of books, mentions are considered. This is because it is not the same that in a book a certain work of another scientist appears cited 40 times or just 5 times. For these researchers who work years on a book, one cannot expect the same number of citations than in natural sciences. If, for instance, in an edited book that contains 20 mentions it means that the author(s) consider that cited work as very important, because the authors found many ideas worth to be cited. That is why in these scientific disciplines a mention contains the exact page where the cited idea can be found. (You would not have to read the whole book to find the cited idea.)
As scientometry started in natural sciences, initially it was not relevant to count the mentions, but later, as scientometric assessments have been extended to humanities, the need of counting the mentions as well became imperative.
For instance the Hungarian Science Bibliography, the database of Hungarian scientific publications (https://mtmt.hu) that also administers the citations, initially it was not capable to store mentions. This was a disadvantage for researchers active in humanities. After many years of development (an a new data storage concept) now it is possible. Beside defining the citing work you can add mentions specifying the page and the citation context (on the same page one can receive several mentions).
This functionality now compensates for the imbalance of humanities and natural sciences.