Consider UIParent like a sheet of glass over the 3D world. Most UI elements will use it as the base "parent" because it is hidden/shown when you press Alt-Z (as is anything parented to it) but essentially it's just a frame.
Templates are just virtual XML frames used as an outline for other frame/widget structures (in XML or created via CreateFrame). If you extract the UI (or use Xrystal's links) you can see in various XML structures the
inherits="xxx" These are the template(s) used as the base structure for the given UI element (some templates will also inherit from other templates).
UIParent and templates are not related.
Widget (frames, buttons, sliders etc.) don't have a traditional inhertence model but you can see an approximation in the first image
here