Antigens and antibodies are not distinct, they are different sides of the same coin.
Blood types are determined by what antigens the red blood cells have. They can have A antigens, B antigens, both, or none. They can also have Rhesus antigens (+) or not (-). This gives the 8 blood types:
A+, A-, B+, B-, AB+, AB-, O+, and O-.
If someone is a negative type, other than AB they will make antibodies to attack the other antigen. Someone who is A- has rhesus and B-type antibodies. If they receive a transfusion of B- blood, the B-type antibodies attack red blood cells with the B antigen, and binds them together into clots. This defeats the whole purpose of the transfusion, as the blood cells are prevented from functioning. In addition these clots can lodge in key blood vessels causing fatal complications.