Clojure has immutability built into the language and the core data structures are all persistent so that you can get sufficiently efficient partial updates while still preserving a pure FP style.

Furthermore, the data structures in clojure also have interfaces that make it easier to swap out which data structure you're using while still keeping whatever map/filter/reduce algorithm implementation you're sending it through.

Common lisp, on the other hand, has setf. Which more or lets you mutate anything. You certainly can code in an FP style in common lisp, but it doesn't restrict you in any meaningful way. Not a problem if you control the entire codebase, but when gluing components together this can be a source of friction.

FP in CL is kind of optional, and it's also more in the sense that you can pass functions as arguments or return functions, meaning FP == First Class Functions.

But in Clojure, FP is kind of mandatory, there's no OO for example, and it's more than just first-class functions, it's also immutability.