The only way to get a BF Upgrade on a domestic flight is if the aircraft is either a 777 or 767 or 752. As those are the Only CO aircraft that have BizFirst seating.

Battlefield is (different opinions) but generally is when you have already taken your seat in the back and the GA comes on board calls your name out and hands you a new BP with a seat up front.

If you get UPed before your flight that is simply what it is being Upgraded, since you'll probably be on some type of 737 it wont be BF but reg CO 1st. A very Big difference in the type of seat and pitch (amount of room between your seat and the one in front of you). This also applies to the 753s, which have reg 1st and not BF.