There are actually 5 address types commonly in use at the moment (P2PKH, P2SH, P2WPKH, P2WSH, and P2TR), and two of them encode a 32-byte (256-bit) value, not a 20-byte (160-bit) one, so the actual number of possible addresses is 2*2^256 + 3*2^160.
You technically can convert between some address types, for example both P2PKH and P2WPKH encode the same type of public key hash. However, you should never do this, because 1) the recepient will almost certainly not monitor the blockchain for payments to the converted address, and 2) they might not even be able to spend coins sent to the converted address, for example if their private key is on a hardware security module that only works for their original address type. Always send to the exact address you are given.
