[SueM loves WDW]

If you have a wheelchair or scooter, you don't need to get a Guest Assistance Card to use the accessible entrance; seeing your wheelchair or scooter tells the cast member you need to use it. The Guest Assistance Cards are basically a way to let cast members know what assistance is needed by people who have invisible disabilities. Some may have a wheelchair or scooter, but also have invisible disabilties (as TalkingHands mentioned).
All of the lines at Animal Kingdom and the Studio are Mainstream lines, which means that the line is wide enough to be wheelchair accessible and doesn't have obstacles, like stairs. This cuts down on people "cheating" when they don't really need a wheelchair. Since, in most cases, wheelchair users are waiting in line with everyone else, there is little incentive to rent a wheelchair unless you actually need one. in fact,sometimes people with wheelchairs actually wait longer because of fire and evacuation rules about how many people with special needs can be on one ride at a time.
Because Magic Kingdom and Epcot are older, some of the lines were not able to be totally wheelchair accessible, so those few rides have a separate wheelchair entrance. As rides have been renovated, new ones added or fastpass added, they have been made accessible, if possible.
For some rides/attractions, the only wheelchair accessible line is the faspass line. People with wheelchair, scooters, canes, crutches, etc will be directed to the Fastpass line for those attractions without having a Guest Assistance Card. This sometimes causes confusion though. Because people went in thru the Fastpass line for some rides, they may try to enter the Fastpass line at rides that have Mainstream Access. When they are told they need a Guest Assistance Card or Fastpass to use <font color="green">that </font> entrance, they assume it means they need a Guest Assistance Card to use the wheelchair accessible entrance.