What you're referring to for the Apple site is your Apple ID and password. You'll use that on your Mac as well for signing in to iCloud and other services like iTunes, Apple TV, Music, for example. When you set up a new Mac, you'll be asked to sign into your Apple ID before you create a user account and password.
The computer's user account and password is just for that computer. You wouldn't use it, for example, to sign into your phone or iPad. You would use your Apple ID for that.
Your Apple ID is an email address. Your computer user account is just a name you choose.
It's a good idea to create a computer user account and password that's different than your Apple ID. It can be something as simple as your first name or Peter's Mac, something like that. If you really wanted to, you could use the same password, but for security purposes, it's better to have something different.
Here's the details about setting up a new Macbook Air so you'll know what the setup assistant will require. If you have other questions, ask away.
By the way before creating new threads, be sure you're in the right forum such as Notebooks for the family of Macbooks (instead of iPad).
Use Setup Assistant to set up your MacBook Air right away, or learn how to set up certain features later.
support.apple.com
