I was playing mine craft this morning and i went to log back in later that day and it was logged in and everything but it said play demo and i don't know what to do.
Added (1). It also says Welcome, player. In the bottom left instead of Welcome "my username"
Try going to a game called "Mineshafter". It's a game that doesn't need downloads and it is free. It's not a demo, it's an updated version with horses in it. You can still play it normally and you will be able to have your own account. Just don't log it out if you don't know your password.