TS stands for tip-sleeve and TRS stands for tip-ring-sleeve (see picture below).
TS cables are generally used for mono, unbalanced signals such as sound from an electric guitar.
TRS cables can be used for mono, balanced signals as well as stereo signals. An example of a mono, balanced signal would be the line in or out from your audio interface. An example of a stereo signal would be what your headphones receive when you plug them into any “headphone” jack.