The LA is the economy engine with bushing bearings instead of a ball bearing crank and a air-bleed carburetor. It replaced the older FP line of engines and differs from the old FP engines mostly by having a rear mounted needle valve. It's not as powerful as the FX and AX engines.

The AX is the more powerful ball bearing engine with a two needle carburetor and rear needle. It replaced the FX which was very similar to the AX.

I have no idea what the letters actually stand for, probably nothing.