Is there a difference between "Background Feature" and a general "Feat"?

Question

I'm attempting to make a custom D&D character, with a custom background. In 5e, backgrounds often feature a "Background Feature" that does not really give them any kind of mechanical advantage; it is used more as a plot device.

For example, in the backgrounds provided in the PHB (Entertainer):

Feature: By Popular Demand
You can always find a place to perform, usually in an inn or tavern but possibly with a circus, at a theater, or even in a noble’s court. At such a place, you receive free lodging and food of a modest or comfortable standard (depending on the quality of the establishment), as long as you perform each night. In addition, your performance makes you something of a local figure. When strangers recognize you in a town where you have performed, they typically take a liking to you.

Is this difference clearly defined anywhere?

Answer 1

Background features are not feats; you're reading the features right as prompts to character development, usually with a tiny easter egg (free passage, access to encampments) thrown in.

Feats, which one might obtain by DM option after forgoing ability increases, are described starting on PHB p.165.