What happens when a transaction script for mining is used for fund transfer?
One is a pay-to-pubkey-hash script (the typical script represented by normal addresses), the other is a pay-to-pubkey script. Both are perfectly valid and standard.

The reason for using direct pay-to-pubkey in coinbases is because they are older. For most purposes pay-to-pubkey-hash is superior (you don't need to know the full public key of the recipient, there is a standard address type for them, there is a marginal security benefit, and they require less space in the validation database). However, direct pay-to-pubkey is just as valid, and the mining code was never adapted to use pubkey hashes instead.