The problem is that the concep of well formed formula depends on the language you are working with.
A language has a syntax, i.e. rules that allows you to "build" terms (i.e."names") and expressions (i.e."sentences").
If I assume that you are working in formalized arithmetic, usualy variable like "x" are terms standing for numbers; so, the expression $x > y$ is well formed. But, in this case $x$ and $y$ are not wff.
If instead we are working with the language of propositional logic, where the variables ($x$ and $y$) are called sentential variables, the expression $x > y$ is not well formed.
Again, we need to know what language are you handling.
About concatenation:
but the comment about concatenation of two wffs not being allowed is really the crux of my issue.
If I work with propositional logic, the language is made by sentential variables, like $p, q, r, ...$ and truth-functional connectives, $\lnot$ (negation, unary), $\land$ (conjunction, binary), $\lor$ (disjunction, binary), $\rightarrow$ (conditional, binary).
The rules available to build expressions are (tipically) :
(i) every sentential variable is a wff
(ii) if $A$ ia a wff, then $\lnot A$ is a wff
(iii) if $A$ and $B$ are wffs, then $A \lor B$, $A \land B$ and $A \rightarrow B$ are wffs
(iv) nothing else is a wff.
Reviewing the above rules, you can see that there are no rules allowing you to juxtapose two wff without interposing a connective; e.g. :
$AB$ and $\lor A$ are not wffs.
If you are working in first-order number theory, you have individual variables, like $x$ and $y$, you have the above connectives, you have the equality symbol and the quantifiers, (for simplicity, we assume that also $>$ is a primitive symbol).
The following are examples of wffs :
$\forall x (x > 0)$ and $x = 0$
Again, you have rules like the above, that do not allow you to "build" an expression like :
$(x = 0) \forall x (x > 0)$
But there are languages ($\lambda$-calculus) where concatenation is allowed; and then there are programming languages ...
