How Armature reaction is different from Self inductance?
It looks like you are talking about alternators (synchronous generators). 

The self-inductance is due to physics of the winding itself and is equal to N^2/Reluctance, where N is nymber of turns of the winding.

However, armature reaction is due to current flowing through the armature winding. It gives rise to magnetic field which distorts the main magnetic field.(the one which is responsible for inducing emf that causes current in the armature winding)

You can remove stator winding from alternator and supply it externally with ac source, then you will find that it has inductance only equal to its self-inductance.

However inside the alternator, while loaded, the demagnetizing effect of armature reaction, actually decreases resultant amp-turns(mmf). And hence terminal voltage of alternator decreases. The demagnetizing effect of armature reaction is represented by an equivalent reactance called "Armature Reaction Reactance", which is different from self-inductive reactance possessed by winding due to it's physical properties viz. length, area of cross section, no. of turns and material.