And since mine does not function 'normally,'
On MacOS X, ps command is "SetUID root" and does not list the ps command itself (without option -a); THIS IS NORMAL (of cause you may think it inconvenient). In most of UNIX and UNIX-like OS's, the OS has a mechanism which allows the ps command to access (without root privilege) to various information of processes currently running in the system. For example, Linux and FreeBSD (and some others?) have "procfs" to allow this. But the current (and all of previous) versions of MacOS X do not have any such mechanism, so the ps command must be SetUID root if it want to access these information. Of cause there are some information which can be accessed without root privilege, and the ps command gives no error messages even if it is not SetUID root (it just can't list some of the information).
does that mean I as a user do not have root privileges?
Even if your account is an admin account (and you know the admin password), your account itself is not the root account. You must supply the admin password when you need a root privilege (unless the command itself has the root privilege through the SetUID root mechanism).
If you have removed the "SetUID" bit from /bin/ps, then the ps command lists itself without the -a option; but if you look into the output carefully, especially if you specify options like '-ax' or '-axe', then you will notice that many information are missing in the output of non-setUID-root version of ps. For example, for the processes owned by other users (such as root), the full path name of the command is missing, and the TIME column is always 0:00.00. On my iMac(Core2Duo), the TIME column is 0:00.00 even for my own processes (on my PowerBookG4 the TIME column correctly shows the accumulated cpu time for my own processes).
If you are satisfied with the output of 'ps -a' (of SetUID veriosn of ps) but just don't want to type the '-a' option, then you can define an alias in your shell startup files (.bash_profile, .bashrc, etc.).
PowerMac G4 Mac OS X (10.4.8)