Lingo. Jargon.  Let me do what I should’ve done before - define a few things in one place.

This is not meant to be exhaustive, but defines the things I commonly refer to in my PITCHf/x posts.

Speed  -  this is almost always “start speed” in MPH.  end speed is also measured.  This is the calculated speed at release
y0 - this is a key number - y is the distance from home plate (which I think is actually at 1.4 ft., not 0).  y0 is the release point.  Actually, it is where the system picks up the ball and starts tracking it.  y0 seems to have settled on 50, but has varied from 40 to 55.
x0 and z0 - what we typically refer to as a release point.  It is where the ball is at y0 (0 is time in seconds, btw).  x is lateral and z is vertical.  0 is the ground for z.  0 is the middle of the plate/rubber for x.  A negative x value is to the catcher’s left, or inside on a right-handed batter.  Most, if not all, of the graphs I use are from the catcher’s perspective.
pz and px - where the ball crosses the plate.  I think Alan Nathan has noted that py is 1.4, as noted above.

OK, now on the the good stuff.  The key thing is how we view the movement of the pitch relative to what a straight/not spinning pitch would do if only gravity was acting on it.  In other words, when we look at vertical movement - expressed as pfx_z - it is inches up or down from what would’ve happened with gravity alone.  I’m not 100% 0 is really 0 here, I need to find that article again ......  pfx_x is horizontal movement, relative to a straight path between x0,z0 and px,pz, that is caused by spin. 

The typical chart is the PFX stuff, which is usually the most telling and tries to capture movement.  It’s sister chart is also derived spin info and includes RPM and Degrees.  That is often helpful is splitting two-seamers and four-seamers, which can look very much alike in a PFX chart.

To identify pitches, I use eyeballs or k-mean clusters.  Google k-mean clusters if you want to know more, but it is a decent way of dealing with this mathematical problem, without being baseball specific (beyond the inputs, which I usually set as speed, pfx_x, pfx_z, rpm, deg).

Hope that helps deciphering my stuff.