You can get all the digimon in one game, yeah. It'll take a lot of playing, though.
Digimon evolve differently than Pokémon and other monster games. Each battle gives you experience and once your mon has enough you can choose to evolve it.
In this image you have Greymon, the big orange dinosaur dude in the center. He probably started as Agumon.
Now, as you see he can devolve back into Agumon OR ToyAgumon, a sort of Lego like variant OR that third Digimon I don't recognize.
He can also digivolve into one of the four on the right, including MetalGreymon, Magna dragon, and SkullGreymon.
Greymon is champion level. To the left is rookie, to the right is ultimate.
Baby, in training, rookie, champion, ultimate, mega is the general flowchart of evolution levels.
So basically you raise a Digimon, generally starting at the rookie or in training rank. You digivolve it to champion once you have, say, level 25 and at least 40 strength to throw some numbers out there.
Cool now it's stronger so you fight with that for a bit.
Hey, you can digivolve again! Cool!
So you do. It's ultimate now.
But what's this? The mega form requires level 80 and 230 strength? But your ultimate has a strength cap of 200. How do you get there?
Easy! Devolve your mon BACK to the previous rank. This will give it some Stat boosts. Yes it reverts its level back but when you train it up again it will be stronger than before. And maybe you'll want to explore a different route on the evolution tree. You can see in the image that Greymon can evolve into four Digimon. Three are available, meaning he can do it now, but SkullGreymon says no go. The digimon doesn't have the stats for it so he'll need to be raised more, probably by a round or two of devolving then evolving again.
Basically, the game, and collecting monsters, is just you leaping around on evolution charts gaining stats along the way and continuously getting stronger and stronger Digimon.