It is not completely different, but rather quite similar [1]. Clojure adds the concept of protocols, which it uses to abstract over cons cells (and it requires that the second element of the cell is an ISeq rather than an arbitrary object).
First, in Scheme, vectors are not made of cons cells.
Second, in Clojure, you can certainly make lists, trees etc. from cons cells. It's just that vectors and maps are more common.
Third, Clojure is not only a Lisp (https://clojure.org/about/lisp), but an exceptionally good one at that. I'm amazed that some people find that controversial. I love Scheme and Clojure, and the thought that they're not both Lisps -- something immediately obvious to any long-time Lisper like me -- strikes me as patently bizarre. Clojure is not only a very good Lisp, but celebrated among Lispers for facilitating Lisp's rise in popularity in recent years.
> When we call cons with two args we get a Java error with a line number?
Clojure requires that the second element in the pair be an ISeq.
> since it is mostly incompatible and lacks a lot of the usual Lisp features.
I and many others disagree, including Clojure's designers, who designed it as a Lisp. Homoiconicity, macros, S-expressions and FP make a language a Lisp. OCaml and SML are about as different as Scheme and Clojure, yet no one thinks they're not both MLs.
> Clojure requires that the second element in the pair be an ISeq.
Lisp doesn't have such a requirement and does not have 'ISeqs'.
> I and many others disagree,
That does not make a convincing argument, since you have never used an actual Lisp - as you recently said.
> including Clojure's designers, who designed it as a Lisp.
Derived from Lisp mostly as a blend of FP, Java hosting/integration and Lisp ideas.
> Homoiconicity, macros, S-expressions and FP make a language a Lisp.
Lists are deprecated in Clojure (for maps, sets, vectors, ...), No interpreter, no Lisp down to the metal, no Lisp in Lisp, no images, core Lisp data structures look different, different API, different syntax, impoverished REPL, strange numerics, Java leaking in many places, lots of compromises because of implementing it on top of a not-Lisp-friendly VM, ...
Lisp derived, but Lisp looks & feels a bit different.
[1]: You can see the implementation of Clojure's cons cell here: https://github.com/clojure/clojure/blob/clojure-1.9.0/src/jv...