I've always thought of it like this:

Aftershave or 'aftershave splash' is a thin, alcohol-based liquid applied to the face after a shave

A lotion is the stuff grandma puts on her hands a couple times a day to keep them from drying out.

A balm is that waxy stuff in a tube that you apply to your lips to keep them from drying out.

The way I was brought up was that an aftershave must 1) have an alcohol base and 2) burn a bit when applied. Secondly, there is no such a thing as an 'aftershave balm' or an 'aftershave lotion'

I think that some of this debate comes from regional colloquialisms we use. In Cental California, I've NEVER heard anybody use the term aftershave-balm or aftershave-lotion...EVER