Are they just forms of Kyurem (like Deoxys-A is a form of Deoxys), or are they completely separate pokemon, with different move pools, abilities, stats, etc...? (Are they separate Pokemon according to the pokedex?)
They are just Forms for Kyurem. Black Kyurem learns Freeze Shock, and White Kyurem knows Ice Burn. Also yes, they are Serperate Pokemon in the Pokedex.