Even though we all speak English, we don't speak the same language
There are many terms that mean the same thing, or almost the same thing. And so, different people will use them interchangably.
Terms that mean that a discrete/digital/bit/boolean/binary register/address/tag/memory location has a "one" in it:
True
Set
Closed
High
Made
Terms that mean it's "zero"
False
Reset
Open
Low
Unmade
This of course, has no bearing AT ALL to the meaning of the -| |- and -|/|- symbols.
In relays and other input devices, -| |- means Normally Open (or N.O.). When connected to a PLC, this will make that register/address/etc. into a "one" (or any other similar word) when the relay coil (or transistor equivalent) has some minimum threshold energy at it.
In ladder logic, -| |- (which in Allen-Bradley, and only Allen-Bradley, is abbreviated XIC) is a logical question, asking if there's a "one" (or equivalent) in that register. If the answer is "Yes"/"True"/"It is", then the instruction "solves as true", and so "passes power". The fact that this instruction is asking a question is exactly why Allen Bradley calls it XIC - "eXamine If Closed" (or "'Check' if 'True'", or "'See' if 'it equals one'", or however you want to phrase it).
Again, the relay -| |- and the ladder logic -| |- have nothing to do with eachother, other than a shared symbol and a shared address. The relay -| |- puts the energy there; the ladder -| |- reads to see if the energy is there.
Clear as Mudd?