JSTOR - coverage of about 2,600 journals. Most recent years may not be available, but good for historical research (time span covered: 1665 to nearly the present).
General databases - these include scholarly journal articles, but also include other sources such as magazines, trade publications, newspapers, theses, etc. Generally, there is a tab, or another way to limit your results to just the scholarly or academic journal articles. [Primary research articles are just one type of scholarly article.]
Citation databases - these do not include the full text of an article, only the citation information and the abstract, if available. Usually they will include links to the full text article, if the library has access to it in another database. Examples:
PubMed - contains 34 million citations for biomedical articles back to the 1950s. You can limit searches to full-text articles and to scholarly publications. Many citations include links to the full-text article in other library databases.
Scopus - contains 87 million records covering more than 23,000 journals. Time span covered: 1788 to the present.
Web of Science - contains 84.8 million records covering 21,100 journals. Time span covered: 1900 to the present. (You must be connected to the university's VPN when off campus to use Web of Science.)
Too many articles or too few articles?
If you get too many articles in your search results, you need to narrow your focus. Add another term to your keyword. If you can't think of one, look at the keywords used by the database or find the keywords in an article seems to be close to what you want. In an article, keywords are usually above or below the abstract.
If you get too few articles in your search results, you are probably using too many keywords in your search. Try removing the least important keyword and doing the search again. Check the spelling of your keyword(s) and look for alternative spellings (e.g., peroxisome was once called microbody).