Stroking would be a generic term to describe all types of groundstrokes and volleys.
As in forehand stroke, backhand stroke etc.
Ballstriking would be a term more commonly used in golf
However in the 21 century tennis has developed into a power game and "forehand strokes" 50 years ago looked weak compared to the forehand drives in the modern game.
Stroking the ball denotes a less aggressive defensive action to the ball where the object to keep the ball in play.
Striking sounds more like a power stroke , in essence a offensive attack where the object is to end the point.