> Even if you convince me these two languages are so different, there's nothing here to convince me Common Lisp deserves the title of the "real Lisp" or "true Lisp"
It's the lineage of Lisps where Common Lisp is in, which is Lisp:
Lisp I, Lisp 1.5, Standard Lisp, Interlisp, Maclisp, New Implementation of Lisp, ZetaLisp, Spice Lisp, Common Lisp, Emacs Lisp, ISLisp, ...
Those are all compatible to some extent and share a common core. Code moved a lot along these dialects. Macsyma had been written in Maclisp, moved to Zetalisp, then to Common Lisp. Reduce was written in Standard Lisp and then was ported to Common Lisp (without adoption). Hemlock was written in Spice Lisp and moved to Common Lisp. LOOPS was written in Interlisp and then moved to Zetalisp and later Common Lisp. CLOS was written in Common Lisp and was moved to Emacs Lisp and ISLisp. Even much of Common Lisp was moved to Emacs Lisp. ISLisp can be implemented as a package in Common Lisp relatively easily (Kent Pitman did this to check that ISLisp is compatible and has nothing which is not 'easily' implementable).
It was also usual that some Lisp implementations ran multiple Lisp dialects side by side, sharing everything: data, memory, I/O, ... For example Interlisp-D had a Common Lisp implementation side-by-side with Interlisp. The Symbolics Lisp Machine ran Zetalisp and four variants of Common Lisp side-by-side.
Then there are a lot of derived languages which either have different syntax, different semantics, different data structures, etc.
Examples are Logo, MDL, Scheme, Racket, Dylan, ML, Clojure, Javascript and a bunch of other languages.
Scheme initially shared some code with Lisp. Dylan tried it with a Lisp transpiler, ML initially was written in Lisp, ...
> Scheme can also run LISP code from 1960 with a very small driver.
The old Scheme is relatively near the Lisp mainstream, the newer Scheme less and less. Twenty years ago there was some code sharing between Lisp and Scheme, now almost none.
For me there are two definitions of Lisp:
* the main line compatible and sharing Lisps
* the general abstract family of Lisp which share an undefine subset of a set of features: lists, s-expressions, lambdas, parentheses, ... But you can find lots of languages in the larger Lisp family which have only a rough subset of this, like Javascript or Logo.