It's actually kind of tough to say whether or not that's an exact match based on the model numbers alone because Shimano often makes a couple variations of a given model.
However, cranksets are more or less universal (at least, more so than things like shifters and derailleurs). There are only a couple of things that you need to watch out for.
- You need it to work with your chain. If you have a 9-speed chain, you want to get a 9-speed crankset. If you're not sure what you have, count the rear gears.
- You probably want the same number of gears. It's possible to switch to a two-speed crank, but since you mention that you're a newbie, it's probably more hassle than you want to get into. Single speed may be possible too, but it's even more of a hassle.
- You want approximately the same number of teeth. Derailleurs have a minimum and maximum chainring size that they'll work with. You'll have some range though and if you decide to change to a bigger or smaller crankset you'll probably have to move the derailleur up or down.
- You need it to match your bottom bracket spindle. It looks like those are both square taper, so you should be good there.
- If you do need to replace the bottom bracket as well you'll want to make sure that the one you get is the right size for your bottom bracket shell. They're usually 68mm or 73mm. Some bottom brackets will fit either size. You'll also probably want the same spindle length. You have some leeway with a geared bike, but it's easier to just make sure it all matches.
Within those constraints, you'll find that you have a whole lot of options. One of those options is probably the crankset that you're looking at, but you'll have to check all that stuff to be sure.