I'd like to tell you what kind of pump I have, but without pulling it out, I don't see any identifiable marks that would give me a hint. The pressure switch thingy looks old and unmarked, and I would guess has nothing to do with what type of well pump it is anyway.
If you have an Amp clamp (meter) you can use it to find out how much current it draws. This will not only be able to give you a good idea as the the HP, but how much power it will take to run. Many amp meters will also record the highest (inrush) current that the motor pulls to get going.