An American oyster list usually reads as a list of places rather than of varieties. That convention exists because the meaningful differences come from the water rather than from genetics.
One species covers most of the coast
The great majority of oysters harvested along the Atlantic and Gulf coasts belong to a single native species. A Gulf oyster and a New England one are close relatives, not distinct types.
Naming the species would therefore tell a diner almost nothing. Naming the growing area tells them what conditions the animal grew in, which is where the variation lies.
The Pacific coast complicates this slightly, since several species are farmed there, but the same place-based naming convention is used for the same reason.
Salinity is the strongest single variable
Oysters are filter feeders that take on the character of the water around them. Salinity drives the mineral, briny quality that dominates first impressions.
A bar near the mouth of a bay sits in nearly full-strength seawater. One a few miles up an estuary, where a river dilutes it, produces a distinctly milder oyster.
Because river flow changes with rainfall and season, salinity at a given site is not constant, and the same bar can taste noticeably different across a year.
Temperature drives texture and condition
Cold water slows growth, and slow-grown oysters tend to be firmer and denser. Warm water accelerates growth and produces a softer animal that reaches size faster.
Spawning also matters. Oysters direct energy into reproduction when water warms, which changes texture and is why cooler months have traditionally been associated with better condition.
Farming method changes the shell and the meat
Bottom-planted oysters grow in the sediment and develop heavier, irregular shells. Oysters raised in floating or suspended gear are tumbled by wave action, which produces deeper cups and cleaner shells.
That tumbling is a deliberate technique. Regular disturbance breaks the thin growing edge and directs the animal's energy into thickening and deepening the shell instead.
How to read a list usefully
A list ordered from mild to briny is doing the work for you. Where it is not, asking whether a given oyster comes from near a river mouth or from open salt water is the most informative question.
Harvest areas in the United States are classified and monitored by state shellfish authorities, and closures follow water quality conditions rather than the calendar.
That regulatory tagging is also why every oyster served commercially can be traced back to a specific area and harvest date.