The three major distinctions are:
1. the straight draw when the cue ball returns along the path it took to the object ball.
2. the freezer, in which the cue ball stops where the object ball was.
3. the side draw, when the cue ball moves along a path perpendicular to the directional contact between the cue and object ball.
Can anyone explain how to induce the three different shots, or discuss the conditions needed to re-create the three different types of draw?
First of all, your stroke must always be the same. It must be accelerating and smooth, with a nice follow-through. The spin is derived from the tip. To be more precise, the tip, when contacts the CB, compresses. If your stroke is moving straight forward smoothly accelerating, the compression of the tip is bigger as it contacts the CB for a longer period of time. Take a ball, put your index finger and push the ball lightly with it while maintaining the same velocity with the finger. You will see that the ball will very soon stop making contact with your finger and roll forward freely. If you make the same thing, but with an accelerating motion, your finger will always remain in contact with the ball. Now imagine doing this with your cue (accelerating and pushing forward aka follow through). If you have a nice accelerating motion, the time where the tip is contacting the CB and is compressed against it is greatly increased. Therefore, more "spinning energy" is passed to the CB. The softer the tip, the more it compresses, so the more it can spin the ball. (note that by spin, I mean english and draw and follow)
This stuff is easier to say than actually do them. Good cues and tips can be bought, but they are no stores where they sell a good stroke. The weight of the cue must do all the work when cueing, You will see many inexperienced players grabbing the cue with their thumb and their index, or by grabbing the cue with more fingers, but with their grip wide open. (fingers not "closed" enough) These are approaches of the principle that you must always grip your cue lightly in order to let its weight do all the work. You will not see many pros doing that but you will notice that their grip seems pretty solid and not loose. They grip the cue firmly and steadily but lightly at the same time. It is a difficult thing to describe actually, but you will find that by gripping the cue with a solid grip (do not put strength on your fingers, just close them together while lightly touching the cue), your aim and cueing will get more stable and less error-prone and if you manage to do this while playing with the weight of the cue (like throwing it forward) you will achieve good action on the cue ball. You will see that many times if you play a fast shot (not strong, there is no such thing as a strong shot, only a fast one, as the velocity and acceleration are the only things that matter when cueing) your hand will slip and the cue will move forward a bit. This is completely normal and it is a strong weapon in your arsenal. I try to always have this stuff in my mind when I am cueing. You will have to learn things on your own and find out what is suitable for YOUR GAME. Pool in many aspects is a matter of personal preference. Do not take any of the things I say (or anyone if he is not an instructor) for granted but consider them. If you think that your technique works, keep it. But try other things too. Do they help? Does it help if I press my finger more? Does it help if my arm makes a bigger arc? Etc. etc. Through trial and error you will find your way.
Of course there are many players who have an unorthodox way of gripping the cue. Bustamante has an ugly grip but this grip has "terminated" lots of players.
So. The draw shot. Your stroke must be the same. If it is draw, follow, stun or whatever. If you have a straight in shot and want to freeze the CB then you can do this with an infinite type of ways. You can put very little bottom spin and play fast, or cue with the tip almost touching the felt (danger of miscue) and play really slow. This is also called a drag shot, or a kill shot. You will hear the (beautiful) sound of the draw, see the CB rotate back like crazy, but with the very little velocity, the CB will arrive at the OB without any spin and freeze.
If you want to draw the CB at a straight line, you will do it if your fundamentals are correct and your cue is moving straight. You will just have to be cool, relax, do a nice follow through with lots of bottom english and if your aim is true and not cheat the pocket at all, your CB will roll back at the same line like it has a string attached on it.
This "side draw" you are saying is achieved if the CB and OB are not aligned with the pocket, or when you cheat the pocket intentionally or not. You can set a straight in shot and try to shoot the OB at the left or right side of the pocket with a stun shot. A stun shot is achieved with a spinless CB. You can do it by executing a stop shot but with the cheating of the pocket, the two balls collide off center and the CB will travel along the tangent line. If the CB arrives fast and spinless it will travel a longer distance. Therefore if you want to cover a long distance here, play a fast shot with not so much bottom spin. This can be done with every shot. Every OB has one and only a tangent line which the CB can travel on regardless of the initial position of the CB.
The greatest achievement in this game is having a good and beautiful stroke. All the other stuff will come and find you, as long as you play often and focused, if you have a good stroke (aim, position etc.). But the stroke...is something that you will have to find on your own. And of course you will be changing it throughout your entire playing life. Listen to every opinion and find out what's good for you. Good luck.