Below is a dictionary for fishing, written in the UK with the differences in terminology for BrE/AmE. That said, the first thing is whether this is saltwater or fresh water fishing.
A rod with a fishing line is said to be cast into the water. (cast, cast, cast). "Oh, that was a great cast!" "Where did you learn to cast like that?"
In freshwater fly fishing, the nice broad motion of getting the line into the water is considered an art and it is called: casting. That is because a spinning reel is not used. If using a spinning reel in fresh or salt water, casting is very easy. Without a spinning reel, it is not easy and you have to learn how to handle the line and reel.
However, in both cases, a fish is said to strike (go for the bait), whether in fishing in saltwater or freshwater on both sides of the pond.
At this level, there really is no difference in terminology.
fishing terminology with BrE and AmE terms
this is when a fisherwoman or fisherman gets a bite from a fish and lifts his or her wrist upwards with a snap in an arc in an attempt to set the hook into a fish
Setting a hook:
striking at a bite to set the hook into the fish's mouth.
To set a hook you snap your wrist upward which will lift the line. The line (the rod) is then lifted as a result of the wrist motion.
Please note: When you get a strike, you never, ever yank or jerk the line. That is a sure-fire way to lose a fish. The hook will not set. You raise the rod from your wrist in one single motion. You snap your wrist to set the hook. (Please note: the word snap is tricky as when a line breaks it is said to snap).
Basically, when you get a strike in freshwater fishing, or angling (fly fishing), you raise the rod from a 45 degree or slightly higher angle in one motion of the wrist. This is called setting the hook. In ocean fishing off a boat, when a fish strikes, they usually start to run so the hook sets itself. This can also happen in fresh water when you are fishing off a boat.
setting a hook
british-englishtag if you want answers that are specific for your country (I get from a comment that you're British).