If you ask me, I think the meaning of a square disk's color is the equivalent of the meaning of a floppy disk's color. Of course you could take advantage of different colors and give them meaning (whether you had labels on the floppy disks or not) to help order some data you wanted to put on the floppies. I think the same could be said for TOS disks, so my final thinking is that they could have meaning, but is up to the person using 'em.
To make an example, lets say I worked on the (NCC-1701) Enterprise's computer core. In my quarters, I have six yellow disks, six blue disks, six red discs that I can freely use on my computer. If there are no way to label these disks, I'd narrow down what I want and organize data by color-coding. Recreation (games and literature) can be blue as blue's my favorite color. Work can be red, considering that since I have an enginerring-specific job and I would wear a red shirt (but luckily live through the five-year mission!). Yellow can be for keeping up with personal stuff, like messages from a loved one or something as it's left over from the two other color choices.