POSIX stipulates a number of commands are available (see the Shell & Utilities volume) and that they work in a certain way. Here are those commands:

admin alias ar asa at awk basename batch bc bg break c99 cal cat cd cflow chgrp chmod chown cksum cmp colon comm command compress continue cp crontab csplit ctags cut cxref date dd delta df diff dirname dot du echo ed env eval ex exec exit expand export expr false fc fg file find fold fort77 fuser gencat get getconf getopts grep hash head iconv id ipcrm ipcs jobs join kill lex link ln locale localedef logger logname lp ls m4 mailx make man mesg mkdir mkfifo more mv newgrp nice nl nm nohup od paste patch pathchk pax pr printf prs ps pwd qalter qdel qhold qmove qmsg qrerun qrls qselect qsig qstat qsub read readonly renice return rm rmdel rmdir sact sccs sed set sh shift sleep sort split strings strip stty tabs tail talk tee test time times touch tput tr trap true tsort tty type ulimit umask unalias uname uncompress unexpand unget uniq unlink unset uucp uudecode uuencode uustat uux val vi wait wc what who write xargs yacc zcat

GNU coreutils (what GNU/Linux distributions ship) contains all these commands but they have developed away from the standard POSIX base over time. Some offer better features. Some work in slightly different ways. These coretils versions are what the standard man pages cater for.

But it is still desirable to write scripts that work on many platforms. For example, if you tried to use extended coreutil functionality of grep on OSX, you'd run into syntax errors. And this is why knowing how the POSIX version works is desirable. Install manpages-posix and you know everything.

It's also essential to know this stuff if you're planning on improving GNU coreutils.

Plan9 is different yet again. It was never designed to be POSIX compatible. It strives for an amount of POSIX compatibility through a emulation layer and the man pages for it are again, there as documentation to let you know what you can use.