When you hear people refer to "masters candidates" or "phd
candidates", what exactly does that mean? Is this just another name
for "masters students" or "phd students", or does it have another
meaning? I am asking because I am matriculated
in a graduate program that leads to a masters in my field, but would
prefer not to refer to myself as a "student" when I advertise certain business
services, if in fact "candidate" means the same thing. Thanks.

All masters/PhD candidates are students, but not all students are
candidates.  A candidate is a student that has completed all of the
requirements for the degree except for the dissertation itself.  In my
own experience, I wasn't a "candidate" until after I had passed my
second year candidacy exams (aka qualifier exams, etc) and was working
solely on my dissertation.