The cut fastball been an increasingly popular pitch in the past decade or so. Most pitchers that use the cutter have worked it into their repertoire as a secondary pitch, but there are some exceptions - the most notable, of course, being Mariano Rivera, who throws a cutter the vast majority of the time.
The simplest (and admittedly somewhat inaccurate) way to explain the cutter is to say that it’s sort of halfway between a slider and a fastball. It’s got more movement than either a 4-seamer or a 2-seamer, but doesn’t break down the way a slider or curveball does. Instead, it mostly breaks in towards the pitcher’s glove-side (as opposed to a changeup, which breaks back towards the pitcher’s arm-side). Velocity-wise, it also tends to fall between a fastball and a slider. As a Sox fan, I’ve seen lots of cutters from Jon Lester and Josh Beckett, and they tend to hover in the 87-89 mph range. Compare that to their low-to-mid 90s fastballs and 75-85 mph breaking balls.
Ultimately, in terms of speed and movement, most baseball pitches fall along a simple continuum of speed and movement. 4-seam fastballs fall on one far side (maximum speed, minimum movement), and the 12-6 curve falls on the other (minimum speed, maximum vertical drop). So the continuum roughly goes as follows, from high speed/ low movement to low speed/ high movement:
4-seam fastball
2-seam fastball
Cut fastball
Slider
“Slurve”
Curveball
(A few pitchers, like Jonathan Papelbon, even throw what they rather unfortunately refer to as the “slutter,” which - you guessed it - is between a slider and cutter in terms of speed and movement.)
In practice, actually throwing the pitches isn’t as simple as the continuum implies, since it takes distinct grips and wrist motions to execute each pitch effectively. But in terms of what the ball is doing on its way to the plate, the continuum sums things up pretty well. Of course, there are other pitches like the changeup or knuckleball have their own distinctive traits that don’t fit perfectly into the continuum, and my description above doesn’t differentiate between left-to-right vs right-to-left movement, but that’s why pitching is so complex. 