Why are there different types of diapers?
For different circumstances and needs of course. If you are referring to cloth diapers and disposable diapers then here is the answer. Cloth diapers, the first diapers invented and have been around for almost as long as humans have. They are arguably more comfortable and better for a baby's skin but require a lot of laundry work, are bulky, stiff and make it harder for the baby to move and may be uncomfortable when wet since they don't absorb as quickly as disposable. Generally they are more suited for and work when at home but not when out and about.
Disposable diapers, a more modern innovation are thinner, more discreet, more flexible and less inhibiting on the movement of a baby and absorb more quickly than cloth but are arguably less comfortable and more likely to cause a rash than cloth.
If you're talking about taped baby diapers, pull-on baby diapers, training pants, older children diapers and adult diapers well taped baby diapers are more suitable for less active babies, pull-on baby diapers are more suitable for very active babies who love to move around a lot, training pants are much thinner and much more underwear-like to help toddlers transition to underwear when toilet training, older children diapers are for kids who have a bedwetting problem or other toiletry issues and adult diapers are for elderly people and those with incontinence.