More precisely, the distinction would seem to be that programs in the tree calculus can analyze themselves with reference only to the reduction rules of the calculus, not needing to reach for some meta-language or theory outside the calculus that works on source code or some AST representation of the program [0]:
Reflective programs are programs that can act on themselves to query their own struc-
ture. The querying is important: that the identity function can be applied to itself does
not make it reflective. A simple example is the size function defined in Chapter 5.
When applied to itself, the result is (the tree of) the number 508 [...] Self-evaluation
in a calculus provides good evidence for the ability to perform program analysis and
optimisation within the calculus itself. Traditionally, self-interpreters were allowed to
act on the syntax tree of a program, i.e. its quotation. [...] When quotation lies
outside of the formal calculus then interpretation is separated from computation proper,
so that some sort of staging is required.
A demo of a size function is given here [1], implemented directly in the tree calculus:
What he implemented IS quotation, despite his objections.