All of the above responses are excellent. What I would add are a couple of things I've seen in officiating and match-directing a fair number of both types of matches.
First of all, if you've not been in modern pistol competition before, you're going to find out that, very likely, your gun-handling habits are not that good.
My experience suggests that USPSA is the most rigorous about the safety habits and application of them, with IDPA close behind. The USPSA Range Officer program goes way deep into safety issues and IDPA, the relative newcomer, followed closely. I don't intend to malign any other discipline with generalities, but I've been to a whole lot of matches and the big lesson you're probably going to get is that you don't have near as good a set of gun-handling habits as you think.
When I went to my very first match, I believed I was a competent gun handler of thirty years safe experience, and well-prepared to handle my old Colt 1911 under match, or any, conditions. Within an hour I was disabused of that notion completely.
Here's why. Public matches, where just about anybody able to make it down the driveway can gun up and go, have some pretty stringent gun handling rules that are enforced quite closely, much more than any other environment. It has to be that way, just because... we don't know anybody, and what they know.
Muzzle direction and finger location are the two big obsessions. As an RO who's run lots of brand-new competitors (who still had lots of shooting experience), I can tell you, very few folks have muzzle and finger discipline sufficiently ingrained. This is often the result of years or decades of just going to range and shooting, usually with friends, and no particular enforcement beyond just a loose sense of common sense.
At an organized match, you'll hear about it instantly if your muzzle strays beyond the "180", that theoretical cone from where you are to the back of the range, 90 degrees around in all directions.
And if you let that trigger finger stray into the trigger guard while you're slamming a magazine home, there's a good chance you'll hear the dreaded range command "Stop!".
But, you will quickly realize that all this will make you a far, far better gun-handler, and it all soaks in quickly.
Another new concept to many new match participants is the "cold range" thing. Basically, you may never, ever handle a gun, with two exceptions: at the designated, official "safe area", and only then without ammunition either present or being handled, or on the actual firing line, at the very specific range command including the magic words "make ready".
I can't tell you the number of times I've had a new competitor step up and yank his gun out once he's in the start box. It's a DQ- a disqualification, and you're out, completely.
DQs are a draconian-seeming thing, especially at first, but, again, you'll see the sense of it in short order.
I put all this out there not to hector, but to prepare folks who haven't done this before. I only wish I'd been so informed in advance- I almost (and should have) got DQed in minute #1 my first match, because I didn't know any of this stuff.
So... watch the muzzle, watch the finger, and in a short time, you'll be having more fun with a gun than you ever did before. It's going to all fit together soon.
And you will be much, much better for it.