USCU...unfortunately, there are not universally defined terms for what you've asked. Generally, HMA is characterized as either "Open graded" or "dense graded". Open graded mixes are generally used for friction courses and have larger top size aggregate, much higher voids, and essentially "gap" grading. Dense graded mixes have a more uniform gradation and may contain larger top size (3/4") or smaller top size aggregates (1/2" or 3/8")
Each state DOT tends to define their own based on what has worked in that state. Some states use viscosity grading for their asphalt cement, some use penetration grading (in my experience, more popular). It depends on the leanings of the state materials engineering group and the requirements of traffic, durability, material sourcing, etc.
In general, mixes with a 3/4" top size aggregate would be consider "coarse" mixes, with 1/2"-3/8" being in the "medium" gradation range, and smaller coarse aggregate being in the "fine" gradation range...below that would be sand-asphalt hot mixes.
The mix structural properties do not change significantly for dense graded mixes between "coarse" and "medium" gradations. Both can achieve significant stability and durability with proper design.