I'm confused about why you would differentiate between vegetables and carbohydrates. That's like differentiating between a car and the engine within a car. Vegetables are mostly carbs and water.
It doesn't refer to cruciferous/fibrous veggies, as well as things summer squash, even though they are almost entire carbs, because the carb content per serving in these foods is quite low - low enough that you can probably eat as much of them as you like and still be within the prescribed range.
When people talk about avoiding carbs, they don't mean fibers.
My personal strategy is not counting but ranking and never eat something worse if I can eat something better. So I could roast some potatoes, but why not just buy carrots that are practically on the same shelf at the store?
Low carb diet does make a big difference losing weight but watching net calories makes a bigger difference. If you're 500 calories under the maintain level. You'll easily drop a pound a week. Combine with some light daily exercises and you get that close to 2.