How do these flavors of liquid smoke differ?
Mesquite is a very assertive flavor that typically goes with beef, especially fatty beef.

Pecan and hickory are stronger than apple, but milder than mesquite, and are great for pork or poultry, and work just fine with beef.

Applewood is very flexible, a bit lighter and sweeter. It's the only one of the woods you mentioned that I would consider using with fish.

Ultimately, there's no hard and fast rules - taste things and do what works for you!