I want to create a text to display the score for my game and the space shooter tutorial uses a GUI text to do so, but it has the message “This component is part of the legacy UI system and will be removed in a future release.” So should I use this or is there a better alternate solution? And what is the difference between normal text and GUI text?
I’d think of it like, as long as your score is in a variable then you just have to change it later when you have to. I’d worry about fixing it after you finish the tutorial. It will probably still work for some time. So learn now, don’t get too paranoid about deprecation until you are making a commercial product. 
But when you get there you need to be "using UnityEngine.U"I and a Text type which can hold the new GUIs Text Component. Usually you start by just creating a Canvas with a Text component, either in the editor or procedurally. GetComponent to reference it (or make it public and set it in the inspector) and use its .text property to change what it displays.
Oh, and to answer the last part, I think it’s the difference between the new GUI system and the old way. I don’t have much experience with the old way though.