A 'command line interface', for example for bash, does the same. What is the difference to a REPL? Is it just another name for the same concept or are there differences? What do you think?
It is a subtyping relationship. Bash's command line is a (minimalistic) REPL, but not all REPL are like Bash's command line. In most contexts, talking about REPLs is implicitly talking about REPLs that do more than just read, eval and print, however illogical that may sound.
Note that few languages actually define READ in a user-friendly way (since python 2.6 you have the ast package, Bash's "read" returns strings).