We have compressed and uncompressed addresses, because the public key can be either compressed or uncompressed.
When bitcoin addresses were introduced for the first time, they were all derived from uncompressed public keys. In 2012, it was decided to generate addresses from compressed public keys to decrease the transaction size.
An uncompressed public key includes 130 characters, while a compressed public key includes 65 characters and takes less space.
But then how can we identify compressed and uncompressed addresses?
If the address is yours, you can know that with checking the public key or the private key.
If the address is not yours and there's outgoing transaction from the address, you can know that with checking the raw transaction.
If the address is not yours and there's no outgoing transaction from the address, there is no way to know whether it's compressed or uncompressed.