BB means Blockbuster. Those are the super moves you equip.
BB1 is a level 1 Blockbuster. (You can equip several different BB1s at once)
BB3 is a level 3 Blockbuster. (You can only have 1 BB3 equipped. They have two skulls on their icons)
SM is a Special Move. (You can equip as many copies of these as you want)
All blockbusters and specials can be found in three ways:
Playing the Daily Events
(SMs and BBs of all levels will drop randomly, can be won in Treasure Fights and for completing the Event)
Ranking high in Prize Fights [PF]
(you can see what specific SMs and BBs will be given out by checking the PF Rewards)
Opening SM/BB Relics
(There are different types of SM/BB Relics that will give you Bronze / Silver / Gold Relics. These can be bought using theonite, and are given out as rewards for various fights and events. Note: It is not recommended to buy these relics. Save your theonite for characters!)