Depending on the design details, an amp labeled "Class A" may under some extreme circumstances move to Class AB operation. These conditions usually involve load and power demand.
One way to look at it is that in a push-pull power stage the higher the bias (within limits of course) the longer the stage stays in Class A operation before moving into Class AB. Class amps run with very high bias to stay in Class A under most operating conditions.
Pure Class A is the limiting case of this situation. The stage is designed and biased so that it will not move out of Class A operation under any normal operating conditions.
Note that be definition all single ended amp stages are Pure Class A. If the stage move out of Class A it clips.
In practice the difference is mostly marketing.
