Q: Difference Between iCloud and Macbook Password

So I recently got a new Macbook Air. I have had Apple Products in the past so I had an Apple account, but I decided to change the username (I didn't enjoy signing in with my email from 4th grade, yikes.) So I did all that smoothly, changed the password and all. However my computer keeps asking for my iCloud password, but with my old email. I tried entering my password (and old password in), but it wouldn't let me in, just kept saying the password was wrong. I tried "signing out," but when it did that, another screen came up asking me to enter in a password to actually get into the computer. But it wanted my iCloud password as well, which it obviously won't let me use. Not only this, but I have to restart my computer to actually get in it. When it goes to sleep, I can't enter in any password to let me get in, but when I restart the computer and enter in my old password, it lets me. I don't understand any of this, is there anything I can do? I know there's a lot to this question, but thank you for any information you can give me!!