Hi Alison,
There are three resorts that you are considering.
Disney's Animal Kingdom Lodge is a traditional resort hotel, offering traditional hotel rooms. Both of the resorts with "villas" in the name are Disney Vacation Club Resorts. This means that the rooms are villas, and offer different configurations, some of which include more bedrooms, kitchens, and living space.
Disney's Animal Kingdom Villas - Jambo House are villas included in the Disney's Animal Kingdom Lodge main building.
Disney's Animal Kingdom Villas - Kidani Village is located next to Disney's Animal Kingdom Lodge and Disney's Animal Kingdom Villas - Jambo House. You can book villas at the Disney Vacation Club resorts using traditional methods such as a credit card.
The decor at all of these resorts is rich and beautiful, and themed to African culture. Outside of windows nearly everywhere, you can see exotic animals. I spoke with a cast member who believed that guests cannot use the pool facilities interchangeably. However, you should ask this to a cast member when you arrive as sometimes due to cast discretion, guests are able to use the other pools. At Disney's Animal Kingdom Lodge and Disney's Animal Kingdom Villas - Jambo House, the pool area is Uzima Pool, which is a large pool with a zero-depth entry and waterslide. At Disney's Animal Kingdom Villas - Kidani Village, you can enjoy Samawati Springs Pool and the nearby Uwanja Camp, which is the water play area you are referring to. It is really fun for little ones - my daughter spend hours frolicking there when she was young!
Have a great time planning your vacation Alison, and please do not hesitate to ask if you have any further questions.