There is some confusion here.
POSIX is a set of standards, one of the things it speaks to is the commands, options, and what the options mean.
So, if you go onto a POSIX-compliant box, all of the commands + options mentioned above behave identically. The boxes are free to have other options, if they want, for those same commands.
So your division into "UNIX" and "Linux" may not be a simple as you think. Plus, a lot of the GNU (GNU coretutils distribution) commands that come with Linux have the same base set of options, possibly with extras as well.
Your best bet is to go to
Front Page | The Open Group, search for a command like tr and read the specs, then get a copy of the full documentation set from
Coreutils - GNU core utilities -- compare based on that.
This is an odd enough endeavor to ask: is the homework?