Why do we need two different formats of WIF (wallet import format)? I know that a public key can be compressed. However, a public key and its compressed one have the same private key. Then why do we need two different Wallet import formats for each compressed and uncompressed one?
Wallet software needs to know whether to search the blockchain for an address generated from a compressed public key or not. The encoding of the private key signals which type should be searched for.