Egoist/egotist

My bathroom is equipped with a book of common errors of the English language. It reminds me that "embarrassment" has two r's and two s's and explains the difference between eatable and edible, among other things.

I was surprised but pleased to see that they distinguish between "egoist" and "egotist" as follows:

Both these words are used to mean 'a self-centred person', though strictly speaking there is a useful distinction between them that is worth maintaining.

•  An egoist is a person whose selfishness is based on the philosophical principle that the only certainty is one's own existence, and self-interest is thus a legitimate basis for morality.
• An egoist is a person who is self-important and vain, and talks about themselves a great deal.

This is far from perfect because Objectivists don't think an individual's existence is the only thing an individual can be certain of. Furthermore, I quibble that the definition of egoist uses "themselves" with a singular antecedent.

Nevertheless, I am happy that some random reference book feels that the distinction between egoist and egotist is "useful" and "worth maintaining." Hear, hear!