From the FAA's viewpoint, they have (very reluctantly) interpreted control line aircraft as NOT UAS, because the legislation that was handed down to them interpreted a UAS as an unmanned aircraft system that included a ground station with RF link. A control line airplane does not have that. As such, we are tethered flight. So to answer your question--we are neither.
Now, getting all the FAA personnel to comprehend that (without an Advisory Circular to guide them) is iffy.
From the standpoint of a park, good luck. Our club did it, but it took some serious coordination with an understanding airport manager, cooperation of the FAA tower people, and a very nice lady at the parks department. The park district in question here prohibits all model airplane activity unless approved by the park district president. I would expect that you could go on-line and read all of the relevant rules to figure out the size of the mountain you are trying to climb.
If the playground you are eyeing is school district property, then that is a different set of folks and they will have their own rules and roadblocks.
Good luck,
Dave