But on the same links you sent are saying:

A Linux-based system is a modular Unix-like operating system, deriving much of its basic design from principles established in Unix during the 1970s and 1980s.

What difference are between “*-based” and “*-like”? If the meaning are the same then I’m right, if Unix-based means must be like a fork directly from Unix and not just a copy build from 0, then yeah, you are right. And I think based and like are the same meaning.

Edit:
I also found this image: https://en.m.wikipedia.org/wiki/File:Unix_timeline.en.svg

Unix timeline:

Edit 2:

I just asked to ChatGPT and seems the AI can explain this:

“Unix-like” and “Unix-based” are terms used in the realm of operating systems, particularly in relation to the Unix operating system and its derivatives. While they may seem similar, they convey slightly different concepts:

Unix-like:
- “Unix-like” refers to operating systems that resemble Unix in terms of design, behavior, or functionality, but may not necessarily be directly derived from the original Unix codebase.
- These operating systems typically adhere to Unix-like principles and may incorporate similar features, commands, and programming interfaces.
- Examples of Unix-like operating systems include Linux, FreeBSD, OpenBSD, and macOS (which is based on a Unix-like kernel called Darwin).

Unix-based:
- “Unix-based” specifically indicates operating systems that have a direct lineage or heritage tracing back to the original Unix operating system developed at Bell Labs in the 1970s.
- These operating systems often have their roots in the Unix codebase, either through direct licensing agreements, re-implementations, or forks of the original Unix source code.
- Examples of Unix-based operating systems include various commercial Unix variants such as Solaris, AIX, and HP-UX, which have historical ties to the original Unix.

In essence, while both terms relate to systems that share similarities with Unix, “Unix-like” suggests a broader category of Unix-inspired operating systems, while “Unix-based” specifically denotes those with a direct lineage or relationship to the original Unix system.

So you are right, and they probably wanted to mean Unix-like. But we could still say based as both has some kind of relationship, and that’s why Linux it’s on Unix timeline from wiki.