What is the difference between "home" and "root"?

No.
~ means home of your current account

root is a special user in Linux/Unix with unlimited power.

if you are root, then your ~ may be /root

if you are user, then your ~ may be /home/user

home folder is parent folder of another user that we created using privilege root
root folder is parent folder of user root(created after finish install linux)

all the those users who are administrator users  thier user profiles  are store at root folder and all those users who are normal users their user profiles are stored in home folder.

"Home" folder is where linux store all the standar user folder data
as for "root" in only store for Root user data.

think of it like myDocument folder in windows..in linux we called it home folder.

~ is short cut to point to the user folder data the ~ will pointed to root folder if you are using root user right and ~ will pointed to standard user folder (Home) if you are using standard user.

If you are using Ubuntu as your Linux distro, this concept will be slightly more difficult to understand as Ubuntu doesn't use the root and home accounts in the same way that "classic" linux does.

This gives a good summary of this:
https://help.ubuntu.com/community/RootSudo

In Ubuntu too the concept is exactly the same.  This article is talking about default security provisions.