You are ALL correct.
It's just that the terms "wet" vs. "slippery" vs. "contaminated" aren't always precisely defined and may vary depending on the jurisdiction.
Direct quotation from Boeing FCOM (emphasis added):
A slippery surface is any surface where the braking capability is less than that on a dry surface. Therefore, a surface is considered "slippery" when it is wet or contaminated with ice, standing water, slush, snow or any other deposit that results in reduced braking capability.
In a hierarchy, it might look like:
- Dry
- Slippery
- 2.1 Wet (e.g., <= 3mm of water)
- 2.2 Contaminated (e.g., > 3mm of water)
If the runway condition is reported (as "Good", "Medium" or "Poor") then it is
slippery (per Boeing's definition) and a safety margin is required.
Except, Wet is a special case because it is not "dry" but also not "contaminated". So as an exception FAA/EASA/ICAO rules allow the use of "Wet" performance data if it's available and better than "Good" (but no better than "Dry"). Hence the OPT choices as listed by Derfred above lists "Wet" separately from Good/Medium/Poor.
** EASA considers Damp to be "effectively dry", but the FAA considers it to be Wet.