There are several different accounts of divine simplicity; I have noted this many times. Here are two:
Account #1: Actuality-Based
Composition involves the union of the actual with the potential. God is purely actual. Therefore there is no composition in God; i.e., God is simple.
Account #2: Identity-Based
Composition involves the union of distinguishable nonidenticals. Everything in God is identical to everything else, so that God is identical to all his attributes. Therefore there is no composition in God; i.e., God is simple.
Both, in different variations, have a venerable history, but they are not saying the same thing; they do not understand composition the same way, and they do not attribute a lack of composition to God on the same ground. They also do not have the same implications; for instance, Account #1 is consistent with there being distinctions in God, as long as those distinctions do not involve the union of the actual and the potential; Account #2 is not. To conflate the two accounts, then, is already to have flubbed discussion of the doctrine. Yet they are often conflated. Both accounts have been quite popular at various times; yet again and again we find that people treat Account #2 as if it were the only account of divine simplicity.
There are even other accounts of divine simplicity; Neoplatonist accounts and Cartesian accounts of divine simplicity are both somewhat different from these. Neoplatonist account are more metaphysics-heavy than Account #2, for instance, while Cartesian accounts have a somewhat unusual structure for epistemological reasons. It is important to recognize that while there is a general family resemblance among doctrines of divine simplicity, they are not all the same.
