I would say the most important distinctions are:
Crosswind vs downwind (this is not really an issue as all modern AWE is crosswind)
Lift vs Drag based
I thinks @PierreB mentions this in the Betz’ limit thread. Some AWE utilize the lift force to generate tension that is harnessed as rotation on a ground based winch. Others utilize a force acting mostly in the drag force direction. The power may be harvested by either torque transfer or on-wing generation.
To further classify the systems we have already seen:
Lift based:
- Ground based winch generator (Yoyo)
- Ground based torque wheel (?)
- Ground based vessel/car pull
Drag based:
- On-wing generator (Flygen)
- Torsion transfer ground generator
Further classification could be in the number of generating wings
- Single
- Double
- Multiple, single layer
- Multiple multi layer
Another classification to be made is
- Self erected
- Supported (eg canopy mesh or single lifters)
I believe Yoyo is the correct spelling https://en.wikipedia.org/wiki/Yo-yo