Remote companies can be set up and operate in a variety of different ways. Some of them are more nuanced than others.
Remote-First describes the mentality of a remote company. At its core, it is defining whether employees are remote by default, or in an office by default. Even if a company is hybrid and not fully distributed, they might still be remote-first.
Having a remote-first mentality also usually comes with a strong preference towards asynchronous communication, as well as more mindfulness towards timezones and people's schedules.