Bi-Grid valves were tetrodes but not screen grid valves. We have several in the museum. The Thorpe K4 is clearly identified and is distinctive in that the anode is also a wire helix. The other three lack markings. See Bi-grid, Q Bi-grid and Q Bi-grid.
'Four Electrode', 'Bigrid', 'Screen Grid', 'Space Charge', 'Beam' and 'Critical Distance' valves are all tetrodes but, being designed for different purposes, they have rather different electrode spacings.
Space charge tetrodes usually have the inner grid connected to the base shell and side terminal, and the outer grid connected to the normal B4 grid pin (pin 2). The inner grid is usually of the smallest diameter practical without risk of touching a sagging filament. In these valves the sprung tension to the filament was not yet a feature. The outer grid may be of closer pitch than the inner grid but is not always so.
The construction of Bi-Grids, used for mixing two independent signals, depends on whether both grids are intended to operate at zero or negative bias (in which case both must be of quite open pitch) or whether the outer grid will operate at (nearly) anode voltage, in which case the inner grid may have a closer pitch.
Some valves will work either in space charge or bi-grid mode and around 1924 there was a brief fad for combining both modes in patented reflex arrangements.
The true screen grid valve S625 did not hit the market till 1926/7 and was of rather different construction. The screen grid being a mesh that entirely or nearly enclosed the control grid.