Authorship mostly Jon Roma; some Steve Phillips
There is definitely a standard scheme used by each railroad to show the possible indications shown by each signal, given each aspect displayed by the subsequent symbol. These are usually listed in a road's signal standards and would include rules describing when, for example, braking distance was such that an Approach Medium (or Advance Approach as the case may be) would be required in advance of a Approach signal. I have portions of several signal standards books (including some from the PRR) and they include things such as standard circuits for the various combination of aspects in electrified and non-electrified territory, for AC and DC track circuits, and so on. There is obviously some customization for each plant in order to meet local operating requirements but obviously it makes sense for a signal system to be consistent from location to location.
The filled or unfilled arc used in drawing signal symbols on a plan is used to describe the type of the signal. The basic signal symbol, which for those not familiar with the system, consists of a symbol showing the positions a signal may display, as if it were a semaphore. The basic symbol implies an automatic signal; i. e., one controlled strictly by the occupancy of blocks.

Figure 1 (attached) shows a basic automatic signal displaying the standard red-yellow-green aspects. The double line shows the "default" or "normal" position of the signal, in this case Stop.

An arc drawn to connect the lines representing the positional "arms" implies that the signal is "semi-automatic," meaning that it is controlled by the occupancy of blocks but ALSO is constrained by manual control.

Figure 2 (attached) shows a semi-automatic signal with two arms; it is capable of displaying the high-speed and medium-speed indications when the operator has established a route and when track conditions are conducive to a movement.

The filled-in arc further implies a semi-automatic signal with the "stick" feature. Following the clearing of a signal for a movement and assuming the control lever is not restored to its normal position after a train movement, a conventional semi-automatic signal will reclear as would an automatic signal as soon as the train passes beyond the blocks beyone the signal. A stick signal is wired such that the signal will not reclear after a train movement until the control operator specifically takes action to reclear the signal.

Manual interlockings could be wired either way; the non-stick feature, for example, would allow the levers controlling the signals for straight main line moves to be left cleared during periods when the tower was closed. As trains came and went, the interlocking signals would act as normal automatic signals.

The stick-feature would probably have been more common at busy interlockings, especially those where succeeding trains didn't follow identical routes. This way, an operator could tend to his other duties without having to worry about restoring signal levers to Stop immediately after a train move. Since the operator might be busy handling another train move, this would eliminate the likelihood of having to run the time release if he forgot to restore the signal lever and the signal subsequently recleared for an undesired move.

"T" end
The T-shaped line on the signal arm in the symbol meant that the aspect was NOT automatic. In other words, at locations where the Restricting aspect of a high or dwarf signal was shown this way, it meant that this aspect was controlled entirely without the use of track circuits. The circuitry, of course demanded that the switches be in correspondence with their control levers and that there be no conflicting move lined or within the plant. When so wired, the Restricting aspect remained displayed regardless of occupancy and it specifically had to be withdrawn by the operator when it was no longer needed. This sort of arrangement might be used when several moves were to be made and it was not desired for the operator to have to clear each move.

Figure 3 (attached) shows a semi-automatic signal with three arms. This signal is capable of displaying the high, medium, and slow speed indications. When the signal goes to Stop as the result of a train move, it remains at Stop regardless of block conditions until the operator specifically acts to reclear it.

This signal is also capable of a restricted speed indication, as denoted by the diagonal line in the lower quadrant position. The T-shaped end on the restricted speed indication means that that indication is controlled entirely manually without the use of track circuits. In all likelihood, it would either involve a separate lever or a pushbutton in addition to the ordinary lever used to clear a more favorable signal.

Alphanumeric annotation
Approach-lit (as a prefix)
variant of "A" prefix, apparently stand-alone
Electric semaphore
Mechanical semaphore