The LA series is more of an entry level engine that has bushings instead of bearings for the crankshaft, fairly mild porting, etc. They do work very well for trainers and a lot of sport planes though and they are economical.

The AX series is more of a sport/performance engine with ball bearings, more aggressive porting, larger carburetors and other features. They produce more power given similar displacement than the LA series.

The FX was basically the forerunner to the AX series and served a similar place in the market.

Ringed engines use a metal piston ring just like most other small engines, cars, and other stuff. Non-ringed engines use very tight machining tolerances and special plating/coatings to create the piston seal. Most, but not all, 2-stroke RC engines are non-ringed while most 4-strokes are ringed.