What is the modern term for fly-fishing casts?

Answer 1

There are a number of different casts in fly fishing, but generally speaking, there is the back cast and the forward cast. When several of these are done in a row before the fly lands on the water, it is called "false casting."

A "roll cast" is employed when there is no room behind the angler to make a back cast.

Spey and double handed casting have many different casts that are quite useful in various situations.