Yes, that would be correct.
MAMP, also referred to as your local webserver, is a software used only on your computer to simulate a hosting environment for any website you want to build/design offline. Without this software, you won’t be able to access/develop your WordPress site on your computer offline.
1and1 on the hand, a service I admittedly don’t know too much about, is a live webserver (online) and offers numerous other options for web hosting solutions etc. (this is according to what I briefly read on their homepage)
As for developing a website online or offline is totally up to you and your preferences for what kind of environment you’re comfortable working in.
It is considered best practice though to develop a site locally first before putting your site up on a live server.