The grouphead (or brew group) is the part of the machine the portafilter locks into — where hot water is delivered to the coffee. It matters for two reasons: the type of group tells you a lot about how the machine holds temperature, and it decides which group parts — shower screens and group gaskets — fit, which is a different question from portafilter size.
The main types
E61 — the classic chromed, angular group with a thermosiphon that self-regulates temperature and gives mechanical pre-infusion. Built to 58mm. See the E61 group explained.
Saturated — the group is plumbed directly into the boiler so it sits at boiler temperature, extremely stable (La Marzocco's home machines are the reference). Also 58mm.
Lever — a spring or manual lever provides pressure directly; the "group" is the cylinder and piston (La Pavoni's levers, at 52mm).
Proprietary — a maker's own group that doesn't follow a commercial standard. Breville's 54mm home group is the common example: its parts are Breville-specific.
Why group parts fit by grouphead, not portafilter size
A basket or tamper is sized to the portafilter. But a shower screen (the perforated disc water passes through) and a group gasket (the seal the portafilter presses against) sit in the group itself — so they fit by the grouphead, not the portafilter diameter. That's why two 58mm machines can need different shower screens if their groups differ, and why we key these parts to the group standard rather than a millimetre size.