I have heard both of the terms "relish tray" and "veggie tray" used somewhat interchangeably. It seems as though there is some overlap between the two based on some simple Google Images searches (relish tray and veggie tray), though they do appear to be somewhat distinct. I am left wondering what the real difference is between the two - as well as appropriate (and inappropriate) uses for each.
In my experience a veggie tray will contain mainly raw vegetables perhaps with a sauce or other condiments.
A relish would be made from vegetables by cooking or some other preserving process (such as pickling). So a relish tray would include a range of processed vegetables.
Of course, it would not be uncommon for a single platter to display a mixed array of raw and processed vegetables.
A relish tray is an assortment of pickles, olives and small sticks of celery and or carrots. You might also have chow chow or chutney. Any type of relish like fancy cranberry relish or a little savory you might add to your dinner plate might be on a relish tray.