We label our terminal blocks by the label for the terminal strip and by the signal.
For instance, I might have TB1 and within TB1 I have L1, L2, L3, N, GND.
So my labels look like this TB1(L1), TB1(L2) etc which is exactly what I want.
I put the (L1), (L2) etc marks in manually and allow there to be duplicates.
Sometimes however, a ".0" or ".1" gets appended to the label so I have TB1(L1).0
I see no difference between the terms Properties that are labels the way I want, and the ones that are not.
Sometime the Terminal Strip editor with show the .0 appendation but not show it on the schematic drawing.
The "Show Levels" settings are the same.