Linux real-time has existed for many years, but it's still Linux. That means that it's a big, underspecified project. RTEMS is designed for high reliability embedded environments, especially spaceflight. These systems are smaller and have very high standards for reliability and verification. Linux doesn't fit well in that niche, but RTEMS is very good.

About that:

- Real-time is about guaranteed response times

- What are the guarantees of real-time Linux?

I don't think I have ever read about the latter. Maybe because real-time Linux is barely used where real-time behavior has more important consequences than audio dropouts. And it's difficult on PC hardware with stuff like surprise system management mode intervention, various hardware probably hogging some bus sometimes...