The major resin producers often add -1, -2, etc., to their resin names for small mods that don't affect the basic chemistry too much (e.g. MTM44-1 or 8551-7) but carbon fibre producers do not seem to. The fiber producers will typically add a new designation, e.g. T300 is Toray's old standard modulus (T300J is a very similar variant but a bit higher strain), T700 is their high strain standard modulus, T800 is their standard intermediate modulus and T1000 is their best IM. Toray's high modulus names are typically Mnn, and M50 through M70 are increasing in stiffness and modernness (they add a J for the fibres with most quality). Hexcel use AS2 (their oldest, lowest strain), AS4 (AS4D most recently) and AS7 for their HS fibres, increasing in modernness and strain to failure, and IM6 through IM10 for increasingly modern and high strain IMs.
As far as I can tell no one has a 'gen 2,' and it is not applied to a 'type' of fibre that I've ever heard. They only 'type' distinctions made are high strength (HS, sometimes HT for high tenacity), intermediate modulus (IM, and actuallly stronger than HS), high modulus (HM) and ultrahigh modulus (UHM). Sometimes a distinction is made between PAN-based (made from polyacrylonitrile fibre) and pitch-based (made from mesophase pitch; this type most commonly get to the UHM grade, with an E above 440 GPa, and pitch-based can have the mad electrical and thermal conductivies. See Cytec's K-1100).
I suspect that the 'gen 2' or 'gen II' applies to the structure that the fiber is made into or possibly the vehicle that the structure is on.
