covering word
Definition - A term whose generality and vagueness covers (i.e. includes) a variety of possible, more precise meanings.

Example -
The verb contact as in I'll contact you covers the senses write, speak, email, phone, etc.

Etymology -
The term is an entry in Wilson Follett's Modern American Usage (s.v. covering words). I have no other etymological information about it. If anyone knows anything please let me know.

Oxford English Dictionary -
The term is not in the OED.

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