Does animate dead, command undead, and all similar function spells fall under the summon count or the pet count for determining how many creatures a person can have on the field?
No it does not, but the GM has the right to limit you if you are being annoying with too many creatures. Of course, that limit only exists in Pathfinder Society... if you're playing in a "regular" game of Pathfinder, there's no limit at all to the number of creatures you can add to the mix.