There are many projects that does not use the master branch as default. For example, Next.js uses the canary branch, the npm CLI and many more other projects uses stuff like prod, production, dev, develop, release, beta, head.

The primary branch in git can have any name by design.

In the context of git, the word "master" is not used in the same way as "master/slave". I've never known about branches referred to as "slaves" or anything similar.