How can I be sure I'm buying the right KitchenAid beaters?
Okay, to explain the 'tilt head' vs. 'bowl lift':

On a 'tilt head' mixer, the bowl attaches with a screw motion into the base of the mixer.  The motor portion of the mixer is hinged at the back, so the front of it can be lifted up.  There's a lever to lock the head from moving on the right side (near the motor, opposite the speed control lever).  And if you don't engage it, you can make a real mess



On a 'bowl lift' mixer, the bowl has two little tabs on each side, which attach to two arms that protrude from roughly half way up the mixer.  The motor portion of the mixer is fixed to the stand and cannot move, instead, there's a lever on the right side of the base (near the arms) that will move the arms up and down so the bowl moves instead of the motor portion.



As for narrow vs. wide ... I have no clue what the corresponding measurements are.

And I took the images from an answer from Doug that's been deleted.  If someone has pictures from the other side (showing the relevant levers), feel free to replace them.