How do these flavors of liquid smoke differ?

Liquid smoke is made from distilling actual smoke and so, to some degree, it tastes like the wood it comes from. For example, I can detect fruity apple notes in apple wood.

Of course, the flavor of smoke itself is far more potent than any of the notes imparted by the type of the wood. In my experiments, I have found that any kind of wood (or liquid smoke) will work for my recipes but some of them are complimented by those extra notes. Again using apple as an example. I really like how apple wood compliments smoked pork.

Some woods are more strongly flavored than others. Oak and pecan are milder flavors that can be used anywhere without distracting. Mesquite is more boldly flavored and will be noticeable.

Some of the actual flavor pairings are just traditional. For example, I am more accustomed to mesquite with beef than pork. I can't say it is really better suited except that I'm used to it.

Smoking web sites will give advice on what woods work well for various applications:
http://bbqrsdelight.com/wood-flavors/
This is a good table. It is a BBQ site so it is all about smoking meat. Notice that most woods work well with any kind of meat. There are descriptions of those extra flavor notes that each wood provides. You can use this to tailor your particular dish.

Wow! No one mentions Hickory which is the most often used smoke for Beef and Pork. Mesquite is typically used for fish and chicken. Applewood is for fish