I still don't get what spraying means. What do you mean by "shooting without recoil"? I heard that for snaking there should be a "whip like action". For example if I decide to shoot in lane 2, my man should actually go all the way to lane 1, then "whip" back to lane 2 while shooting. Is this what you mean? You also said that I shoot at lane 2 and the ball goes to lane 1, so it's like a small cut right?
Cut and spray are different, but both of them cause the ball to move at an angle. There's also a third common way of controlling angle, called recoil (recoil is essentially the same as the "brush" used in brush passing).
Cut (also called chip, especially in passing--e.g. "chip passing") is when you hit the edge of the ball with the corner of the man. Bank shots are often hit this way. A stationary ball will move at an angle if you cut or chip it, and you can cut a ball in either direction (away from you or toward you) no matter which way the ball is moving.
You can hit a chip/cut shot with a stationary rod that is only swinging at the ball and not moving toward/away from you (just line it up so the corner of the man hits the ball and swing straight).
Recoil or brush is when the face of the man moves across the top of the ball--the corner of the man never hits the ball, it's all about the friction between the man's face and the ball. Like cut/chip, recoil can move the ball in either direction (away from you or toward you).
You cannot hit a recoil or brush shot without moving the rod in the direction of the recoil/brush.
Spray is simply the momentum of the ball--the ball must already be moving laterally before you hit it in order for it to spray. And you can _only_ spray in the direction that the ball is moving. Indeed, since spray is simply the ongoing momentum of the ball you don't have to do anything to make it spray.
In fact, any shot that you move sideways will automatically have spray on it unless you apply brush/recoil to counteract that motion. This is why newbie pull shooters have trouble shooting against a reverse defense, and why most new goalies who shoot a pull only shoot options that angle toward themselves (either sharply or more shallow angles).
For example if I decide to shoot in lane 2, my man should actually go all the way to lane 1, then "whip" back to lane 2 while shooting
On a snake, the recoil does in fact come by moving the rod back toward (or even past) the center; if you shoot a square shot to the 1-hole, you recoil back to the 2- or 3- hole during the shot to make it square off instead of continuing to angle out. You'll see a similar motion on a good pull shooter, who will move the fod back away from themselves when they're squaring off the shot.
You can also lessen the angle of spray by hitting the ball harder and/or moving it slower laterally. The faster you're moving the ball laterally, the harder it is to square off that lateral motion. The harder you hit it, the less it'll spray.
NOW, mastering recoil is really the key to good square options. But recoil is not always good. A long, square pull is slightly slower to the long hole than a pull that comes 2/3 of the way across and sprays the remaining distance. Many shooters will pick whether to spray or square based on the defense they're facing.
The snake is no different. You certainly need long square shots. But if you're being raced, using spray effectively can speed you up to the corners. IOW, if you're shooting toward the goalie hole (as opposed to the hole the 2-rod is blocking) then you may shoot a spray shot instead of a square to beat him a bit faster.
One final thought on chip/recoil/spray.
Chip shot can get the most extreme angles on shots, but it's nearly impossible to hit consistently. Look at how few pros use chip passing or cut shots up front, or even bank shots--it's not too hard to get to where you can execute it well 80% of the time, but that means you're cutting down your effective possessions by 1/5.
Brush/recoil is perhaps _the_ single most important skill to master to get really good at foosball. It affects passing, shooting, and you need to know about it for defense to be effective.
I've also played some "active" goalies who like to move around a lot. From the diagram, they "shake" the left guy on the borderline of lanes 1 and 2 and shake the right guy on the borderline of lanes 4 and 5. They do this quite randomly, so it's almost impossible to tell when he's gonna go there. They do it without leaving the middle open for more than 0.1 seconds.
This is what good goalies do: they make you have to guess where the hole is and execute to hit it, instead of just taking your time and executing when you're comfortable.
You also said that I shoot at lane 2 and the ball goes to lane 1, so it's like a small cut right?
No, not really. You're hitting the ball straight with the face of the man, not cutting it. But yes, the ball does angle outward.
Would that shot actually be useful?
Not really, at high levels. It's a gimmick that you might use if the goalie falls asleep or something, but it's still not a great percentage in general.