If we have a structure with just relations, then every subset is a substructure? So I was wondering: > If we have a structure that has the universe $A$ and only relations in it, then any structure with universe $B \subseteq A$ and the same relations, IS a substructure? I feel like this is true. If this is true, does it follow that any 2 structures that have the same relations and functions, are each others substructures/superstructures only if the function in the superstructure is closed in its universe.

Yes, any sub _set_ of a relational structure is (the underlying set of) a sub _structure_. Re: your second question, the answer is also yes if I'm interpreting it correctly: if $\mathcal{A}$ is a structure with underlying set $A$, and $B\subseteq A$ is a subset which is closed under the function symbols of $\mathcal{A}$, then $B$ is (the underlying set of) a substructure of $\mathcal{A}$.

Put another way: **the only way "substructure" differs from "subset" is by requiring closure under the function symbols.** (Note that I'm thinking of constants as functions, here - a constant symbol is a $0$-ary function symbol.)