One's public key is known to everybody but his private only to him,
Everybody should be able to encrypt a message and only one person should be able to decrypt it. So everybody will use the receiver public key to encrypt and he will use his key to decrypt (only he should be able to do it).
A signature proves someones identity. With signature only the sender should be able to sign (so others will not be able to impersonate her). Since only she knows here private key she will use it for signing. Everybody should be able to authenticate the signature. So they use the public key which is the only one they know.