Is pressing home the same as repeatedly pressing back until the home screen is reached?
Depending on the application no. Some applications will always reset themselves when you press their icon from the launcher. The best way to 'return' to an application is to long-press Home.
Say you open Messaging, and start writing a message, then press home, the next time you press Messaging, you'll return to where you left off (editing the message.)*
If you 'back' all the way to home, then next time you press Messaging, you'll start as if you've just loaded Messaging (which is still where you left off.) At this point, the Messaging application is still in memory so it can load quicker.
The only things that can keep going are services, but again, if Android needs the memory, it will stop them. They should handle this gracefully, saving their state, and Android will reload them when resources are available.
It's hard to demonstrate this on the N1 (I did try to overload it with the browser and a 3D game, but it just smiled and laughed) - it has a lot of RAM.
* If Android needs the memory being used by the messaging application for another application, it will stop it and free the memory, and then if you reload it, it'll be as if you've pressed 'back' all the way out. This is why you'll notice stuff like 'Saved as draft' when you press home, it's good practise, just incase Android needs the memory.
Sorry that turned into a bit of an essay.
This is the developer docs that explain it all (it is intended for developers,) but it shows the lifecycle of Activities, Services and so on.