A SFX, or Small Form Factor, PSU is not always required with a mini-ITX case. Many offer compatibility with standard ATX PSUs nowadays, which means you don't have to buy special parts. How they fit a full-size PSU in there with your other components, I don't know. It's all pretty incredible how these cases are designed.
That said, you may need to buy a SFX PSU for the smallest of mini-ITX cases. Especially the sort that don't offer space for a discrete GPU and must be fitted with a CPU with onboard graphics instead. In these cases, you'll want to find a SFX PSU that is safe and reliable, but don't worry, there are loads of those nowadays. Corsair, Silverstone, and be quiet! offer multiple SFX options.
There is also the slightly larger SFX-L configuration, which is something to bear in mind, as we've had issues with some mini-ITX chassis dealing well with the broader SFX-L dimensions.