Some functions from ERC-721 interface contain payable modifiers.

function transferFrom(address _from, address _to, uint256 _tokenId) external payable;

I was wondering why it is payable and found from EIP-721 that explains why.

Solidity issue #3412: The above interfaces include explicit mutability guarantees for each function. Mutability guarantees are, in order weak to strong: payable, implicit nonpayable, view, and pure. Your implementation MUST meet the mutability guarantee in this interface and you MAY meet a stronger guarantee. For example, a payable function in this interface may be implemented as nonpayble (no state mutability specified) in your contract. We expect a later Solidity release will allow your stricter contract to inherit from this interface, but a workaround for version 0.4.20 is that you can edit this interface to add stricter mutability before inheriting from your contract.

Does this mean that when a function in the interface includes payable and when it is implemented, it can be changed to anything? such as public, view, pure? or did it mean that it can only be changed to nonpayable which is nothing? I don't get why it is not

function transferFrom(address _from, address _to, uint256 _tokenId) external;

in the first place. Also the definition Mutability guarantees is hard to understand. Can someone explain this in a simpler way please?

Lastly (since I think it is related to the subject), why do I need to change external to public in order to avoid compile error?

function transferFrom(address _from, address _to, uint256 _tokenId) public { }