Distinguishing semantics vs syntactic techniques and the syntax of your semantic domains Consider a denotational semantics from simply-typed $\lambda$-calculus into dependent type theory. Is that actually a (trivial) term transformation into that dependent type theory? After all, type theory has a syntax.

In fact, even set theory has a syntax*! So how do we distinguish a denotational semantics from a compositional term transformation?

Now, let's generalize to less trivial program transformations — say, transformation to continuation-passing style (or store-passing style, environment passing style, ...). You can show the same idea through a non-standard semantics (here, a continuation-passing semantics) or a term transformation into a continuation-passing term, and they're distinguished by a binding-time shift. Again, isn't the non-standard semantics also a term transformation?

This is a concrete confusion which I've observed at least twice:


In my work (on incremental computation) I've used a non-standard denotational semantics into type theory (a "change-passing" semantics). After a presentation of that, Gabriel Scherer remarked (kindly) that for him, that was a term transformation into a dependently typed language.
"F-ing modules" preempts this confusion — they defend their presentation of the syntax of semantic objects.


  Semantic signatures. The syntax of semantic signatures is given in Figure 9. (And no, this is not an oxymoron, for in our setting the “semantic objects” we are using to model modules are merely pieces of Fω syntax.) [Emphasis added.]



*Apparently, some (non-formalists) claim that set theory is not "just syntax", but something ontologically different. I'll ignore this subtle philosophical issue; the only reference I know on it is Raymond Turner's Understanding Programming Languages.
I think I understand your difficulties, indeed if you consider just a programming language both a denotational semantics and a term transformation (into another language) are nothing but mappings of syntactic elements of the given language in mathematical objects (elements of a domain in the first case, terms of the language in the second case).

Notheless differences between these two semantics start to arise if you put an operational semantics in your programming language and so you want that the denotational semantics and term transformations are compatible with this operational semantic.

In the first case you would like that denotation of terms/programs that compute the same results have the same denotation, hence the denotational semantics should associates to operational convertible terms the same denotation.

In the second case you would simply like that the term transformation maps terms/programs in such a way to preserve the derivations (if you reguard terms and reduction/derivations respectively as objects and morphisms of a category you can say that a term transformation should be a functor).
In the first case we lost information about the reduction between terms in the second case we preserve it. 

In the first case semantically equivalent terms are mapped in the same denotation in the second they are mapped just in operationally equivalent terms but the term translation does not guaratee that equivalent terms are mapped in the same term (and usually that's not the case).

Denotational semantics  allows to easily find different terms, supposing that the denotation-mapping is easily computable, in order to distinguish two programs we just need to compute the denotation an see if they are different values.
Nonetheless in this way we lost information about the reductions (computations of our operational semantics) which are instead preserved by the term transformations. 

I hope this helps.