I'm using Friedl's classification scheme for regex engines from Mastering Regular Expressions. I don't know of a more standard survey regarding regex's as implemented in various programming languages. Anyway, from a practical standpoint an NFA has to be implemented as a push down automata in the Von Neumann machines we currently have to allow backtracking to simulate simultaneous exploration of the arbitrary number of DFA states that a single NFA state may represent. That doesn't make Friedl's classification useless.