They have the same meaning. Saliha is correct that it's more common to say "Have you got a boyfriend?" instead of "Have you a boyfriend?" "Have you a boyfriend?" is not grammatically incorrect, although it sounds very old-fashioned.

Both questions are grammatically correct. Both questions have the same meaning. However, native speakers very rarely say things like 'Have you a boyfriend?' in modern English. It sounds very unnatural. Instead, we say 'Have you got a boyfriend?'. This is very common in informal English.

"Have you a boyfriend?" isn't grammatically correct.

The second sentence should have been gramatically: "Have you got a boyfriend?"