How does the combination birth control pills differ from one another?

Very little. Even though the pill makers would like you to think differently, they really aren't that different. Think of pills as cars....The nuts and bolts of how they all work is the same. Some people prefer one car to another. Some people make like on pill over another but this is trail and error. In my practice i generally prescribe the ones that are less expensive.
Different hormones. There are many different pill formulations--with different hormones (typically a synthetic form of the hormones estrogen and progesterone), different doses, and different regimens (for example 7 d of 1 dose combination, 7 of different dose, and 7 more. Many pills have 21 days of hormone pills followed by 7 reminder pills, but some have 24, and 4. They all work by preventing ovulation.