Signals are either 'Controlled' or 'Automatic'.
Controlled signals normally show a Red aspect and will only clear when the signaller has set a route from them (and the interlocking has determined it is safe to do so), and are required where there are points ahead of the signal.
Automatic signals operate purely from the train detection system, though there may be an Emergency Replacement facility on the panel which allows the signaller to hold them at Red. They normally display a proceed aspect and are replaced to Red by the passage of a train and remain so until the train has exited the section (to the next signal, plus it overlap). These can only be used to protect plain line, where the only obstruction ahead is another train.
The historic rule book distinction between automatic and controlled signals was removed some years ago and new plain line signals between junctions no longer carry the old 'auto' plate supplementing the number. In the days when Signal Post Telephones were the only voice comms between driver and signaller, this signage formerly allowed drivers to pass a signal at danger and proceed at caution if they couldn't contact the signaller.
Today's plethora of wireless communications makes that unnecessary, though many older 'auto' signals still carry the distinctive plate. it has no special meaning today. Such modern signals without auto plates may still operate automatically by default, however.
All signals on modern schemes must have a replacement facility, either individually or in groups. Very early colour light schemes did not have this at all, then after some incidents, a rule was introduced that a replacement facility must exist every so often (I think it was at least one signal every 5 miles).
When TPWS was fitted originally, the focus was on junctions, which were perceived to present a greater consequential risk in the event of a SPAD than a signal protecting just plain line, so those signals weren't generally required to be fitted with it.
In the risk model, head-on, crossing and merging conflicts are assigned a higher risk ranking than rear enders.
The risk assessment carried out when TPWS was rolled out determined that the cost does not justify the expense of fitting them.
Originally, each signal was assessed using a standardised process using statistical movement data, length, weight, speed, type and passenger occupancy of all trains that could plausibly conflict in the junction area protected by that signal to determine a risk score.
A threshold figure was agreed that would trigger fitment. It was set so that all signals protecting conflicting junctions and single lines would definitely qualify (Note existing flank protection measures in the interlocking that physically divert a runaway away from the conflict zone can avoid the need for TPWS protection, and junctions that allow divergences only are typically not equipped).
Some other plain line signals did qualify originally, notably those protecting selected platforms with a very busy mixed pattern of stopping and non-stopping services. Subsequent fitment concentrated on buffer stop approaches, permanent speed restrictions and additional overspeed protection at higher speed junctions (TPWS+). ~11000 of the ~40000 signals on the Great British national network are equipped to some extent today.