What is the significance of version byte and address checksum in version 1 Bitcoin address
How could they give the same result? You do RIPEMD160(SHA256(pubkey)). Then you add zero byte 0x0 to this and perform double SHA256. You take the first four bytes and use them as s checksum which means they are control digits which help the wallet determine you didn't misstype the address.

Now you take this whole thing zero-byte+RIPEMD160(SHA256(pubkey))+checksum and you convert it to base58check. Note: zero byte will make the address always start with '1'.

When sender gets a bitcoin address, their wallet converts it from base58check to hex, checks the checksum and removes both the zero-byte and checksum to get RIPEMD160(SHA256(pubkey)). Then it proceeds with scriptPubKey verification.

That's why it is called Pay-to-public-key-hash. Bitcoin address is just a way of encoding a public key hash.