What is the relation between a programming language and the language of its input?
There is no interesting relation between a programming language (the set of words which are syntactically valid programs) and the set of words that are accepted by a program written in said programming language.

Note that it is possible to design a Turing powerful programming language which, as a formal language, is the set $1^* = \{\epsilon,1,11,111,\ldots\}$.

Still, program $1^n$ will accept a language $L_n$ which is completely unrelated to $1^*$. Indeed, by Turing completeness, for any r.e. language $A$ there is some $n$ such that $A=L_n$.

The crucial aspect to consider here is the semantics of the programming language, 
the way we map each program $1^n$ to its behavior, and ultimately to the set of accepted words $L_n$. Even if $1^*$ is a very simple language, the semantics can still make it Turing powerful, so that $L_n$ can be any r.e. language.