"ps aux" would be the BSD syntax -- "a" for "all processes", "u" for "user format, "x" for lifting the "must have a tty" restriction
"ps -ef" would be the Unix98 syntax -- "-e" for selecting all processes, "-f" for full-format listing.
If I remember correctly : FreeBSD, OpenBSD, and NetBSD would support the BSD syntax only, while many other distributions would support both types of syntaxes.