Final answer:
The nicotinic acetylcholine receptor is the receptor to which both α-bungarotoxin and curare bind, with α-bungarotoxin binding irreversibly and curare binding reversibly.
Step-by-step explanation:
The receptor type involved when both α-bungarotoxin and curare bind, but only curare binds reversibly, is the nicotinic acetylcholine receptor. α-bungarotoxin, a compound from the krait snake, binds irreversibly to this receptor, preventing acetylcholine from binding at the synapse, which leads to paralysis by inhibiting muscle contraction. On the other hand, curare, a South American arrow poison, blocks the receptor competitively and reversibly, leading to muscle relaxation and temporary paralysis.