Is it different from the tax you would face if you just realize your gains?

The exit tax doesn't apply to "gains", it applies to the "value of your company" which is calculated in a way that often means you will owe thousands or even millions in money you don't have, and at no time had.

Yes - the value of your company is the gain. It is the money you would have if you sold the whole thing.

It's only a gain if you sell.

Selling a company and paying tax on the profit in tax is a completely different proposition from paying tax on hypothetical profit you haven't made (and might never make) just because you want to move.

Sounds indeed pretty terrible…

Most unrealized gains are a notional value, the realizable gains are often much smaller. The act of realization can cause a crash in value.