The only situation I can think of where it would really make sense to have "TRS unbalanced" connection is if it's stereo. If people are using language kind of loosely, I suppose it might refer to an "impedance balanced" output, which isn't really a balanced output in the narrow sense of the word, though some people call it that, and it does use a TRS jack.
There's a bit of confusion in this thread. If you're connecting two boxes and:
- They both have TS jacks (i.e. both are unbalanced), it makes no difference whatsoever whether you use a TS or a TRS cable. The ring contact on the cable plugs won't connect to anything at either end. This, I think, is the question in the original post.
- The output box has a balanced output on a TRS jack, and the input box has an unbalanced TS jack:
* If you use a TS cable, you connect one side of the output (the "cold" signal, on the ring contact) to ground, which is generally what you want to do.
* If you use a TRS cable, you leave the cold output signal "floating" (attached to nothing), which is preferable for some particular items (which items should note that in their manuals).
- The output box has an unbalanced output on a TS jack, and the input box has a balanced TRS jack:
* If you use a TS cable, you connect the cold input to ground right at the input box's jack.
* If you use a TRS cable, you connect the cold input to ground at the far end of the cable (at the output box's jack), which is perhaps mildly preferable, though not a big deal.
- The output box and the input box both have balanced TRS jacks:
* If you use a TS cable, you connect the cold output to ground, which you don't want to do. What you want to do - since you've got an input box that wants a balanced signal - is connect the cold output to the cold input. By not doing so, you give up your common-mode noise rejection, as well as 6 dB of level that you otherwise would've had
* If you use a TRS cable, you do the right thing.