There are two main differences between "Parkflyer" and "Full Range" receivers. The main differences have to do with the size of aircraft and distance you plan to fly.
A Parkflyer receiver is meant for shorter range than a Full Range receiver. Like the name implies, a "Parkflyer" receiver is meant for a Parkflyer aircraft. One that isn't too large (say a micro or 1100mm airplane, something that doesn't weigh very much and can easily be flown in an open park as example) that you don't plan on flying too far away from you at any time.
"Full Range" Receiver
The Full Range receiver is meant for larger-class aircraft. Any larger sized aircraft that has a wider flight envelope and range (1400mm warbirds and above, 70mm EDFs and above as example) you would want to use a full range receiver with a satellite. A satellite simply ensures signal strength at a longer range and is always good to have that added insurance.
You wouldn't want to fly a 90mm EDF jet with anything less than a full range receiver with a satellite. The same generally applies for any of the larger class aircraft.