Yes but you missed a lot of things of course.

Linux is free software, unlike MacOS or Windows. That means that the software is given users for free, and they can mostly also change it and redistribute it as their own.

This is why there are so many varieties of Linux Distributions, as the used software components are often the same, but they are released in different cadences, have different configurations and behaviors, or different focuses (for example Gaming, Server, Workstation, Lightweight, System rescue, hacking, anonymity).

Free software means that everyone can use it, how they want. Nobody needs to pay, but donations and contributions are crucial. While many big components like the core part "Linux" and others are developed and maintained by bigger corporations (which sell support or systems to mostly enterprise customers), a lot of the Linux software is fully done by people out of love, in their free time.