Type theory and syntax are similar, in that they are inductive rules that determine whether a particular string of symbols is "correctly specified" in some sense.
There is a difference between syntax and type theory. Syntax in programming languages for example, concerns things that do not concern type theory, such as the fact that the statement
if import microsoft.(false ==== 5) then import is "syntactically nonsense". This is not a type error, but a syntax error.
But I'm unsure what the relation is.
I normally think of syntax and type systems as follows: Let $L$ be the set of possible strings of some symbol set $S$. A particular syntax inductively specifies a subset $T\subseteq L$ of "terms" in $L$. e.g. a program is not well-specified if it is not in $T$. A particular type system then makes an additional restriction, by inductively specifying a subset $W\subseteq T$ of "well-typed terms".
But given such a syntax and type system, we can always consider a new syntax which is simply the old syntax plus also has the inductive rules of the type system as an additional restriction.
Therefore it is not clear to me why there is a fundamental difference between a syntax and a type system.
Is my intuition correct? Can we see type checking a particular form of syntax checking?