Yes, above a certain size, companies typically have some formal procedures. But typically those are a fig leaf.
In many labour markets, there's a legal 90-day probation or equivalent. You bet your boots some people get dismissed at 80 days. Or the job was contract-to-hire, and the contract doesn't "get renewed".
But on top of that, literally every company I've worked at or any of my friends have worked at (including lotsa startups, two of FAANG, and some in-betweens) will terminate when they want to terminate. In most non-European labour markets that I'm aware of, there's a penalty for doing so, and the company just pays that penalty and gets on with it.
Sometimes there's more security than that, I've heard (but not experienced). And sometimes the company puts in large effort to cultivate the underperforming employee first (had that happen to me once; they tried and I tried but it didn't work out). But the overwhelming majority of cases of my first-hand and second-hand experience, dleslie's summary is about the whole story:
> The real interview is always the work you do
Thus, probationary periods can be a time of training and growth for the new employee.