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.
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".
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 :)