CITE = You're using a little of someone's copyrighted info via the Fair Use Doctrine.
ATTRIBUTE = You're using as much as you want of someone's copyrighted info that has been openly-licensed.
One of the most important "author's rights" that authors (creators) have under copyright law is the right to be known as the author of what they wrote / created. (Here, 'author' means someone who created any fixed expression of an idea - writing, art, photos, music, etc.)
When authors want to allow someone else to use their copyrighted work, authors license out that work to the other person. It's literally a legal document proving that the author is giving them permission to use it. Money's usually involved, as this is one major way authors can make money from their creations, but not always. Some authors choose to put open licenses on their online works, which cost nothing to use.
A person who uses an author's openly-licensed work must attribute it correctly - give the author credit as the creator. It's pretty simple (easier than citing):
Now, the vast majority of copyrighted information what you use on a daily basis to complete assignments will not be openly-licensed. Instead, you will be using a small amount of someone's copyrighted information, without asking the author or paying for any license, by way of the Fair Use Doctrine.
Since no license is involved, you don't attribute...you cite.