I have a few things to add to the very thorough response given by @RonPorter.
First of all, I agree that many fish, (particularly insectivorous species, and the predatorial pelagic species), will tend to hit or strike at a bait, or (more frequently,) at a lure.
While the word hit is reserved for the fish's action in attacking a lure or bait, it should be noted that the word strike is also commonly used to describe the action of the fisherman in setting a hook. (For example, my fiancé often admonishes me for standing there looking silly, when I should have been striking at the fish that has just taken my line).
With regard to Ron's suggestion that the word "take" describes when the fish actually becomes hooked, I tend to disagree there, because when a fish takes a lure or bait, (in other words, when it swims away with it in its mouth), it doesn't necessarily hook itself (hook up) in the process.
This concept is clearly demonstrated in what happens when a mulloway takes a live bait that you've set out (on the appropriate rig). The mulloway will take the live bait in its mouth and run with it for a short distance, before halting suddenly in order to chew the fish up a bit (to incapacitate it), then flip the partly-chewed fish around such that it may swallow it head-first.
It is only at this point, when the mulloway is just about to swallow its prey head-first, that you should strike at it in order to set your hook. (While the mulloway is running with the bait, you must always allow the line to free-spool; if you place any pressure whatsoever on the line at this point, the mulloway will feel the external input and immediately spit out your live bait).
Moving on, when a fish becomes hooked, there are several descriptors that can be used to indicate where the hook has become lodged.
Ideally, you want the fish to be hooked through the mouth, with the hook entering on one side of the jawbone and exiting on the other side, (thereby giving you a solid or firm hook-up). If the point of the hook does not pass around the jawbone, the fish is said to be lip-hooked, and you must be particularly gentle with it in order to avoid ripping the hook straight through the flesh (and therefore, out of the fish) while reeling it in.
If the fish has swallowed the hook, it can end up being either gill-hooked or gut-hooked, (the latter occurring when the hook happens to set itself in the wall of the fish's oesophagus or stomach).
If the fish has been inadvertently hooked in any other part of its body, (say through its eye, or in its shoulder), the fish is said to be foul-hooked.
To further answer your question of what a fisherman does to ensure that his/her fish doesn't jump off the hook (or shake itself free), the first step is, of course, setting the hook. After a solid hook-up has been achieved, the most critical factor is maintaining pressure on the line. As soon as you allow even the slightest bit of slack line between you and the fish, you run the risk of losing it. This gives rise to the common saying or farewell amongst fishermen: "tight lines!"
A final thing that I would like to point out is that I have never heard anyone use the words lure and hook interchangeably; (i.e, call a lure a hook)... Perhaps that is a localised phenomenon occurring within part(s) of America and/or the UK?
Apart from the lures used in fly fishing, (flies that are tied directly onto the hook), hooks are generally completely separate from the lure body.