cover term

A cover term is a word (or phrase) that provides a more general, legal, or accurate overarching term for a set of dissimilar terms that share a common property. Synonym: category.

"Cover term" may sound like "comfort term" when enunciated poorly or quickly, which might suggest the cover term is being used to make the original word (or phrase) more palatable or less anxiety producing to the audience. While this may occur, it is never the primary objective of using a cover term.

"Shelter" is the cover term for rent, mortgage payments, housing, and so forth.