fewer: of a smaller number
Example: Express lines at grocery stores should be labeled "15 items or fewer."
less than/more than: a smaller amount or degree
Example: The turnout for the game was less than expected.
under and over both refer to spatial designation
Example: The mechanic slid under the car.
Avoid using "under" and "over" when referrring to amounts. Instead, use "less than" or "more than."