Striking vs Stroking
The distinction between 'stroke' and 'strike' is subtle but critical. When you stroke a cat, the deliverable (for the cat) begins at the beginning of the stroke and lasts until the end. When you strike a tennis ball, all relevant goodness occurs during an interval of .05 seconds that occurs after the stroke's completion. Therefore, you must create the control, power, and spin you wish to impart to the ball before contact. The difference between striking and stroking is timing. If you hit the ball while swinging at it, you are stroking. To swing, then hit, is to strike. The difference is cataclysmic. If you stroke a ball, you are making contact before you have finished the stroke, i.e., before you can release the control and spin-producing forces stored in your forearm. These forces make you the master of the ball, but only if you free them before you make contact.
To swing, then hit, is to strike.
When you contact the ball early, stroking it like some pampered pet, you are a 'pusher'. Contacting the ball late, too long after the release of the stored forces, is also problematic since the racket goes through some weird gyrations in the followthrough and the control forces dissipate quickly after release.
Historic Solutions
There have been several attempts in the past to deal with the difficult job of timing the moment of contact to exactly coincide with the release of control forces. Earlier teaching of groundstrokes called for a smooth followthrough with the racket face pointing at the target for as long as possible, which allowed one to contact the ball late and still have some chance of keeping it in play. However, to maintain a continuous course for the racket into the followthrough, you must intentionally omit storing control and spin forces in the earlier phases of the strike, robbing you of beneficial control and spin. Classic teaching of the volley calls for no backswing or followthrough at all, but that leads to a 'block' volley which puts the incoming ball in charge of its destinty. Instead, great volleyers bury the backswing in the reach for the ball then 'slam the brakes' on the volley swing just before contact, sometimes pulling the racket back off the ball after contact. This 'reverse followthrough' is an expression of vigorous deceleration of the racket head that the hitter starts before contact. It is an effective technique for a solid, well-placed volley. Note that the reverse followthrough motion occurs after contact with the ball; otherwise, it would suck all of the control impulse right out of the strike and take all of the control with it.
How to Not Stroke
The key to a timely release of stored spin and control forces is to finish the Explode phase before contact with the ball. Timing the release of forces is easier said than done. The explode phase requires force in opposition to the forces accelerating the racket head towards the ball. This force comes from pushing back on the 'front' foot in many strokes before contact. This action has traditionally been called 'stepping into the ball' but is actually pushing back away from the ball. If you fail to 'step into' a groundstroke, there will be nothing to stop the forward rotation of the hips and shoulders, and you will drive the racket right through the ball. You might step in, but too late for the counter-force to reach the racket head before contact.
If you explode too early, the stored control and spin forces will dissipate before reaching the ball or distort the racket head's flight path, so you will miss-hit or otherwise mangle contact. Absent perfect timing, we must resort to tricking ourselves into doing the right thing at the right time.
Stepping In
The old admonition to 'step into the ball!' is a black pearl in the sense that neither the teacher nor the student know why it needs be done. Most players believe that stepping-in is a technique for 'adding weight' to a strike as if the velocity of your body is added to the velocity of the racket head to increase the pace of the ball.
The hallmarks of snap are painless power, a pleasant ping, and perfect placement.
One doesn't have to do a bunch of math to see the fallacy of that notion, but at least it encourages players to step in early in the stroke, which is coincidentally the right thing to do. The actual utility of stepping 'into the ball' is to stop or slow the forward rotation of the hips and shoulders, thereby letting the racket head catch up to the wrist under the influence of the stored muscular forces in the forearm. If you are swinging hard, the counter-force needed to reverse that acceleration can be considerable, so a good, hard pushback from the front foot is necessary. The trick is when to step in, and the best I can do is to say that you must take that step in plenty of time for the force wave generated by your feet to propagate through your body and reach your wrist. Finding that timing requires trial and error - which is all for naught if you can't distinguish error from success. Success means a release of stored forces into the ball, and the indication of success is the 'snap' of the wrist. The hallmarks of snap are painless power, a pleasant ping, and perfect placement.