Are labrum and rotator cuff exercises the same? Would I be strengthening both by just doing rotator exercises?  

Different...same. The labrum is a piece of connective tissue that olds the humerus (arm bone) into the shoulder. This cannot be fixed with exercise...If it needs repaired it would require surgery. However, strengthening the rotator cuff mucles does stabilize the shoulder, which is sometimes enough to avoid surgery.
Labrum vs cuff. The labrum is a roll of specialized cartilage tissue that surrounds the rim of the socket. In essence it provides depth to the socket by creating an elevated circumferential rim. This provides better suction fit and stability of the ball and socket joint. The rotator cuff also helps stabilize the ball into the socket. Cuff exercises can help stabilize the joint but labrum may need to be repaired.
No. Some of the exercises overlap but they are different anaatomic abnormalities requiring specific appdroaches.