BG: gravity before the boil; an important all-grain measurement
OG: original gravity at the end of the boil; this will be higher than the pre-boil gravity due to boil off. As wort is boiled away, the amount of sugars in the remaining wort is concentrated.
SG: specific gravity. This can apply to any of them. It's lazy internet speech.
T or FG: Terminal or Final Gravity.