Looking at MattJ100's link (http://pubs.opengroup.org/onlinepubs/009695399/utilities/gre...), it seems like POSIX grep actually does not have any recursion.

Hence, only lubutu's comment ("-R is the recursion flag for ls, cp, rm, etc") is true, while _delirium ("-R is the POSIX-standard flag for recursive grep") is wrong, which means AIX is free to do whatever it wants with both the -r and the -R flags.

That would be kind of perverse given how cp behaves for -r and -R