I order mine "wet" and not "dipped" because I like the bun to not fall apart. From my experiences here's what I've seen:
Dry - they will let the beef drain off it's juices before putting the beef on the bun
Wet - they put the wet beef on the bun and you'll get some gravy but not enough that the bun falls apart. Note: the bun will fall apart if you get it to go and wait 15-20 minutes, since the gravy will have enough time to set into the bun.
Dipped - they put the wet beef on the bun then dip both ends of the bun and typically run the bottom of the sandwich through the gravy. This is best eaten immediately.
When you order, you'll state the type of sandwich (beef, combo), how you want it served (dry, wet, dipped), and the type of peppers you want, if any (sweet, mild, hot). The sweet peppers are just green peppers, the mild and hot are giardenera.
So next time, if you're eating there, say - "beef, dipped, hot."
If you're taking it to go, "beef, dry. gravy on the side and hot on the side" and do it yourself at home.