Awhile is an adverb meaning "for a short time," and it never follows "for" because that meaning is already built in. While is a noun meaning a period of time, or a conjunction meaning "during" or "although," and it's the word you want after "for a." So it's "stay awhile" but "stay for a while."
The core difference
Awhile is a one-word adverb; while is a noun or conjunction, usually paired with "a" or "for."
- awhile — for a short time: Let's sit here awhile before heading back.
- while — a period of time: We waited a while before the doctor called us in.
- while — during the same time that something else happens: She read a book while waiting for the bus.
How to tell them apart
The test that works almost every time is to check what comes before the word. If there's a "for" in front, you need the two-word noun phrase a while, because "for" already needs an object to attach to. If there's no "for," the one-word adverb awhile does the same job on its own.
This confusion shows up constantly in casual writing because "for awhile" sounds fine when read aloud, even though it doubles up the meaning of "for." Swapping "awhile" for "briefly" is a reliable check: if "briefly" fits, awhile is correct; if it doesn't, you need "a while" instead.
