Yes, many fonts use double story 'a' for roman and single story 'ɑ' for italic. Calibri, Segoe UI, Times New Roman, Droid Serif, Merriweather, Consolas, and Source Sans Pro are examples I found from quick searching.

... wow, how did I get this far in life without noticing that. a a a a. Edit: Apparently Verdana doesn't seem to do that.

Many fonts having "real italics" would use a different shape, whereas those with only "slanted fonts" would not (like Verdana). It's only a rough rule, but you can assume that most serif fonts will use "real italics".

The words you're looking for are italic and oblique :-) One is a different design, the other simply the same letterforms slanted.

To be honest, I wasn't :) For those not familiar with terminology, they might think that "italics" represents both (because eg. most software would use one or the other if you click on the slanted "I"talic button), which is why I differentiated between "real" or not real italics.

And while I agree "oblique" is a more technical term, "slanted" is frequently used to mean the same thing, and is probably more understandable. Perhaps I am wrong and it isn't :)