In NYC a "regular" coffee is most often used to mean size (10-12 oz is regular) although it would also mean milk, 2 sugars to most coffee servers in take out places delis, breakfast carts, diner counters, etc. If you are sitting down like in a restaurant, the coffee would be brought black and milk and sugar served on the side. I drink mine "large, milk no sugar" and unless I'm a regular somewhere they always repeat back "no sugar?" "Light & sweet" means extra milk and extra (3-4) sugars, and you can of course get any combo (light/no sugar or black & sweet, etc).
The real thing here is know your order before you get to the front of the line - everyone will loose patience with you if you hem & haw and delay everyone else's coffee - its ok to not know the lingo, but not to not know what you want. We have enough tourists and immigrants here, so long as you can say how you want it, regardless of any slang like "regular" or "light & sweet" etc, you are ordering it correctly.