So I started to learn theory of computation and in the class we talk about languages and many-one $\leq_m$ reductions. e.g if $A \leq_m B $ then if $x \in A \implies f(x) \in B$
We say that different languages may be reducible to one another. I am curious how this relates to reduction that we have done in algorithms class. E.g $SAT \leq 3CNF$ or $Hamiltonian Cycle \leq TSP $
Are these problems considered to be languages??? I am confused because we are talking about some similar things as reductions, but now we talk about languages over the alphabet $\sum$ and not NP problems and I am curious if NP problems are actually languages as well.