what's the difference between my "Apple I.D." and my "Apple User Name"? I have trouble signing in because of this

On these forums, you normally sign in using your AppleID. The user name is created and used in the forums since you would not want your email on display in a public forum.

Some years ago, an AppleID could actually be anthing you wanted to use (it did not have to be an email address), but for quite awhile now, an AppleID can only be an email address. For most apple services, you just use that AppleID=email address for everything. But for the forums, you get the user name as an alias to display who you are here in order to protect the privacy of your email address.

Your Apple ID is typically an email address that may be associated with @me.com or @mac.com although it can be any other email address. A password is also associated with an Apple ID. See Apple IDs and iCloud

A username is normally associated with your user account on your computer that you setup when installing OS X or when you first configured your new computer. This is not your Apple ID, usually.

What is difference. Do I sign in with a user name or I d. What is difference.

You sign in with your Apple ID because that is what your account is under. And the difference between it and a user name was explained above.