for two languages in $NP$ does one of them karp reducible to another?
The theorem, as stated, is false: if $A=\emptyset$ and $B=\Sigma$, then we cannot reduce either of them to the other. If take either of $A,B$ to be non-trivial problems in $P$, the claim is true, which is not hard to show (see here). If either of $A,B$ is NP-complete, then the claim also holds by definition of NP-hardness. 

So, the only case left is for problems $A,B\in NP-(NPC\cup P)$, the NP-intermediate problems. Note that such problems exist if and only if $P\neq NP$.

It would not be very surprising to me for two NP-intermediate problems to be incomparable, but this would be very hard to prove, as we currently do not have a good idea of what problems even could be NP-intermediate. So, it would seem that the full answer to your question is an open problem, but if I had to guess then I'd guess the answer is no.