For Direct2Drive and Impulse, you buy the games, download them through their specific download manager, and after that the game is sitting on your hard drive. You can run the manager to install updates etc, but iirc you don't need to be running it to actually play the games.
Steam is slightly different in that you need to run any game you buy on Steam through Steam. This usually means you need to log in to Steam whenever you want to play anything. There is an offline mode, but I know that some people have had issues with it, partly because you used to need to log in before you could put yourself into offline mode... which didn't really work if you had no internet. I'm not sure what this works like now. This also means that if you're Steam account gets hacked, or you forget your password etc, you won't be able to play any of your games.
I really really like Steam. I buy nearly all of my PC games through there, when I can. They have some awesome
sales, and there is stuff discounted every other week. Steam also has really good community functionality. You can chat to anyone currently online, and join games your friends are playing if they support Steamworks (eg. you can join a friends server if they're playing Team Fortress 2, from the main menu). You can create and join community groups which can run live chat rooms. I used to get into all of my Left 4 Dead games through the chat room for a Penny Arcade group which would usually have 30+ people in there looking for games.