Solar = Tiny & Small galaxies
Galactic = Medium & Large galaxies
Universal = Huge & Gigantic galaxies
Military = military victory
Civil = everything else
That's pretty much it prior to TA except for the fact that the Universal Military category includes *all* galaxy sizes and victory conditions so that it basically corresponds to the "regular" metaverse.
TA introduce two new conditions; the immense map and the ascension victory. I assume that immense maps are grouped in the Universal class and ascension victories are considered civil.