Leaf Vegetables are not just vegetables that have leaves, because virtually everything we call a vegetable (with the obvious exception of mushrooms) has leaves at some point even if they're trimmed off before we see them.
Leaf Vegetables, instead, are vegetables whose leaves we eat. We don't eat the leaves off of sweet corn, or potatoes, but we do off spinach. That makes spinach a Leaf Vegetable.
Other examples of Leaf Vegetables are Bok Choy, Cabbage, Chicory, Cress, Endive and Lettuce.
Some people class celery as a Leafy Vegetable, but you could argue that even though the leaves are good and should be used in cooking, most of the leaves are trimmed off at the store because the primary purpose in buying celery is to eat the stalk. (Some people would also counter by saying that celery is barely a vegetable.)
Dark Green Leaf Vegetables
Leaf Vegetables are usually green (except for those that have been blanched, such as Belgian Endive), but some are distinguished further by being called "Dark Green Leaf Vegetables".
The darker the leaf, the more Vitamin A, Vitamin C, and calcium the leaves will have. Also, the darker the leaf, the more "vigorous" the taste, which is why it's more of a battle to get people to eat them. Which is a child going to eat first, Iceberg Lettuce or a spinach leaf?
Chicory, Dandelions, Kale, Mustard Greens, Spinach and Swiss Chard are Dark Green Leafy Vegetables
Leaf Vegetables are often just called "Greens", though some people reserve the word "Greens" for Leaf Vegetables that get cooked, as opposed to eaten raw.
All cooking Greens need a thorough washing to remove dirt and sand.
Some, such as spinach, just need braising or steaming for 3 minutes,
others like Kale and Collard benefit from much longer cooking times.