They are two different things.
Anyone and everyone can be a food critic, no qualifications necessary and no standard in requirements. Getting paid for it is another story. You have to have a hook at a publication. I’ve see local news paper food critics that would give a Papa Johns Pizza 3 stars as long as the advertised with them. To be a “serious” one you would probably need a pretty deep resume as a cookbook author, chef, restaurateur, but there are no real requirements.
In a recent Restaurant Nightmares TV show Ramesy said there was an important “Food Critic” in the house that night. In reality the woman had worked as a pastry chef and was surprised they represented her as a “Critic”.
A Food Judge, or more precisely in the US there is a _title_ called “ACF Approved Culinary Judge”. They judge formal culinary competitions. There are probably other organizations with similar positions. Here is a _link_ to the requirements to be certified by the ACF-
http://www.acfchefs.org/Content/events/Competitions/Judges/default.htm