What is different about the different types of cues and shaft tapers?
Shafts are made with various tapers, the two most common being the pro taper and the European taper. The pro taper has the same diameter from the tip to 30–35 cm (12-14 inches) toward the joint, at which point it begins to widen. The European taper widens continually and smoothly from the ferrule toward the joint. Despite their names, the continually sloping European taper is found in most North American bar and house cues, and not all professional players prefer a straight pro taper on their custom, two-piece models.
Cues can up to a 14mm tip, and lots of Break/Jump cues, or Break cues, or Jump cues have a 14mm tip because a bigger tip is better for Breaking and/or Jumping. Break cues commonly have a Conical taper (also called European) for added stiffness.
A Break/Jump cue is one that is used for Breaking and Jumping with part of butt coming off so that the shorter Jump portion can be used. Jump cues/portions are commonly 40″ long, the minimum length they can be.
Leather tips are better for control, but Phenolic tips, which are harder, are better for power and/or lift when jumping. I have a J&J Break/Jump cue with a phenolic ferrule/tip combination that I like a lot, and they can be bought for $60/65 dollars. I used to believe in separate Break cue and jump cue, but the J&J Break/jump changed my mind about that, and a Break/jump combo takes up less space in your case. Phenolic tips do some getting used to though, and almost require a center ball hit.
A standard taper started out 8-10″
A pro taper started out 10-13″, now is 13-15″
An European taper is like a long cone shape, with no part of the shaft being the same diameter at any 2 points. (constantly tapers down to the tip).
There is also a straight taper, which a lot of Snooker cues have.