What is stored on the Xbox Console, hard drive and Xbox Live

What is stored on the Xbox Console, hard drive and Xbox Live

Please be patient with me. I am a mom not a gamer. We have a Xbox 360 S w
250GB that we are having to exchange for a new one. I have several
questions.
1 - What is the difference between the 360 S and the 360 E (i believe
stands for Elite) Would this be an "upgrade"
2 - What is stored on the console - hard drive - Xbox Live
3 - What needs to be done to save everything so that it can be transferred
or re-downloaded to the new Xbox.
4 - Is there anything that won't transfer/ be lost?
Thank you. Mom