2.4 was the Linux version that introduced "threads" as we know them (discussed here). And CLONE_THREAD is the flag to ask clone() for a thread instead of a process.
Prior to that Linux only had a "processes"... and the word "thread" was historically used to refer to any parallel execution. So historically a process was a form of thread.
The wording in the clone page can be read as explaining the new concept of threads (as we know them now) to an audience that understood everything is a process. As such this clone() wording is very out dated. But not "wrong".
You should generally expect "thread" to refer to its more modern meaning, especially where both "thread" and "process" are mentioned together.
But beware! The Linux community still retains echos of a time when there was no distinction, and "thread" still gets (erroneously) used to mean process... I know of no other system call documentation example of that.