I play tenor saxophone and clarinet and, let me tell you, the transition from clarinet to tenor sax was a little "awkward" for me.
Basically, the fingering for the tenor sax is only similar to that of a clarinet to some extent, so they aren't totally the same. It takes a while to get used to it.
Regarding the embouchure, it is slightly different. Always have a tight embouchure and for low notes the mouthpiece should be more in your mouth (and less in your mouth for higher notes).
Unlike the clarinet, it is harder to reach the lower notes on the tenor saxophone than is is to reach the higher notes.
Both instruments are in the key of B flat, so you can play clarinet music on a tenor saxophone and visa versa.
If you get really good on tenor sax, you could even try bass clarinet (I play bass clarinet too). Tenor sax and bass clarinet are in the same key (B flat) and they use the same reeds. Personally, I love tenor sax. It seems easier than clarinet.