Trying to understand the different types of insulin pumps

I have been reading about insulin pumps and keep seeing different terms like conventional pumps, patch pumps, and hybrid closed-loop systems.

At first I thought they were just different brands of the same thing, but it sounds like they work differently and may suit different people. I am trying to understand what actually changes between these systems.

For people who use pumps or have researched them, what are the main differences between these types? Is one approach generally more convenient, or does it depend on the person's needs and lifestyle?