The difference is that SSL was the name for the protocol Netscape invented, and TLS was the name for the protocol that went through a standardization process. SSL 1.0 was Netscape-internal and horribly broken. SSL 2.0 was less so, and after that came SSL 3.0. Then the standards process renamed it and released TLS 1.0, then TLS 1.1, and then TLS 1.2 (and there's now TLS 1.3 under development).
Those TLS versions identify themselves in the handshake as if they were SSL 3.1, SSL 3.2, and SSL 3.3, in fact.
It's basically just like how Windows NT went from 4 to 2000 to XP to Vista to 7. It's just marketing/politics, and the underlying technical version number just kept steadily ticking upwards (2000 was 5, XP was 5.1, and Vista was 6) with no regard for marketing.
Those TLS versions identify themselves in the handshake as if they were SSL 3.1, SSL 3.2, and SSL 3.3, in fact.
It's basically just like how Windows NT went from 4 to 2000 to XP to Vista to 7. It's just marketing/politics, and the underlying technical version number just kept steadily ticking upwards (2000 was 5, XP was 5.1, and Vista was 6) with no regard for marketing.