TeXmacs in Chez Scheme

I see that Chez Scheme is listed as a “radical alternative” to “consider the embedding of a full-fledged Scheme compiler” in https://texmacs.github.io/notes/docs/scheming.html

If I understand correctly, Chez Scheme could also perform compilation on the fly and run as an interpreter. I wonder what is the technical difference between such and a “true” interpreter?

Your question made me curious and I made an Internet search. I found one page with an explanation that I felt I partially understood, that is the Wikipedia one about interpreters (see https://en.wikipedia.org/wiki/Interpreter_(computing)#Compilers_versus_interpreters).
Let me quote the sentence which seems key to me (especially the first sentence):

A compiler can thus make almost all the conversions from source code semantics to the machine level once and for all (i.e. until the program has to be changed) while an interpreter has to do some of this conversion work every time a statement or function is executed. However, in an efficient interpreter, much of the translation work (including analysis of types, and similar) is factored out and done only the first time a program, module, function, or even statement, is run, thus quite akin to how a compiler works. However, a compiled program still runs much faster, under most circumstances, in part because compilers are designed to optimize code, and may be given ample time for this. This is especially true for simpler high-level languages without (many) dynamic data structures, checks, or type checking.

My question about the “difference” is focused on the TeXmacs part - I mean, what is the difference between migration to S7, say, and to Chez Scheme? Is the later essentially more difficult?

I think that @mgubi would be able to answer your question.