TRS (Tip-Ring-Sleeve) is the name often given to the connector, rather than the cable as such, though of course they would usually be used with a 3-conductor cable. This could be used for stereo purposes, but it could also be used for other things : e.g. as a mono send/mono return for an insert effect (like a compressor on one channel of a mixer), or as a balanced signal carrier.
If you had a stereo output socket (TRS) and plugged in a mono plug with only the tip and the sleeve, you'd be grounding one of the channels (probably the right, which is usually wired to the ring) which is not a great thing to do (https://sound.stackexchange.com/questions/25577/stereo-and-mono-cables-and-jacks-what-happens-when-you-cross-them), and you'd only get the left channel coming over the cable. If you were to plug a stereo (TRS) plug into a mono (TS or TR) socket, you'd get your mono signal coming down either the left or the right channel (probably the left, as this is usually the tip), but you'd leave your right input channel 'floating', which is not ideal.
When it comes to balanced or unbalanced audio, many sockets are designed so that plugging in a TS jack gives you an unbalanced connection, while a TRS allows a balanced connection to whatever's at the other end of the cable.
In summary, you're unlikely to do any harm mixing up stereo and mono cables, but it's a good idea to know the contact arrangement in the equipment you're plugging into so you can use it as designed.
EDIT re. your equipment
Yamaha mg124cx : http://www.yamahacommercialaudiosystems.com/downloads/manuals/mixers/mg/mg124cx_manual.pdf
Focusrite Scarlett 2i2 : http://d3se566zfvnmhf.cloudfront.net/sites/default/files/focusrite/downloads/7317/scarlett-2i2-user-guide-v2.pdf
The Yamaha manual says it has "TRS phone-jack type balanced outputs"; the Focusrite manual says "Set the LINE/INST switch next to the socket...to LINE if you are connecting a line level source such as the balanced output of a stage piano via a 3-pole (TRS) jack." (but for 'stage piano' there, we can read 'mixer')
So my guess is you want to get 2 TRS cables, one for left and one for right, and with a bit of luck that should give you balanced, stereo connection.