Great. You can just say, ‘Care in a hospital falls into three main categories: regular, serious and urgent”

This can work, but it’s not 100% clear what you mean, so you might want to specify afterward. For example, “Airline tickets fall into several categories: first class, business, premium economy, economy, and basic economy.” Now that I think about it, there are a lot of categories!

Perfect! There’s a famous quote in English by the author Mark Twain: “I didn’t have time to write a short letter, so I wrote a long one instead.” It’s sometimes harder to write less than to write more.

Thank you, I’m too wordy. The project tasks fall into three categories: research, design and implementation.

Great use of “fall into” – it might be simpler to say, “The project tasks fall into three main categories…”