My interpretation and what I use for DnD campaigns:
Inn - sells meals, alcohol and rooms. The modern equivalent of a hotel that has a restaurant and a bar. Rooms by the night.
Wayhouse - sells rooms, no meals. The modern equivalent of a Motel. Rooms by the night or longer period. Often has a Tavern nearby.
Tavern - sells meals and alcohol. The modern equivalent of a restaurant. When it closes, all patrons leave.
Alehouse - sells mostly alcohol (mostly beer but some wine) but also some food. The modern equivalent of a Bar / Grill / Pub.
A wench could mean a serving girl in an inn. Could also mean prostitute.
The two terms are not necessarily exclusive. I could see an inn for travelers offering food, bed, and company in bed using the same staff.
https://www.vocabulary.com/dictionary/wench