You have the C major scale. C is the root note, or tonic. It’s the most important note. All the other notes in the scale want to be that note. If you are in D Dorian, you are using the same 7 notes (A B C D E F G), but now D is the tonic. It’s a very important distinction to make.

Here is a simple example to help you hear this for yourself:
Play the song “Drunken Sailor” in D (it will start on A). That is a legitimate Dorian melody. You will only use the notes D E F G A B and C. The song will end on a D note, and you’re fine with that. It’s ending on the tonic, everything is nice and resolved, it sounded great.

Now play the song “Happy Birthday” in C (it will start on G). That’s a major/Ionian melody. Stop on the second to last note (which will be D). Are you okay with that? Does it sound good ending there? Of course not! It sounds terrible! The melody practically demands to resolve to the tonic (C).

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We already said that the C major scale has the notes C D E F G A and B in it… all the naturals. Every one of those notes all over the entire guitar is part of the C major scale. There are many different ways you can arrange those notes across the guitar as well. That’s how you come up with different scale shapes/fingerings.

What that website is showing you are 7 different position shapes (meaning that your hand will not move up or down the neck) for the major scale. Each one starts from a different note in the scale.

The diagrams are not that great, as they do not make it clear what the horizontal and vertical lines represent. For the record, the horizontal lines are the strings (bottom to top = thick to thin); the vertical lines are the frets (ascending left to right)

The first shape starts from the root of the major scale. So if you started playing that shape from the C on the 8th fret of the 6th string, you would play the notes C D E F G A B C D E F G A B C D E. The shape will stop at the 12th fret of the 1st string. You may play a total of 17 different notes, but it was all A B C D E F and G… just 7. The 7 notes of the C major scale.

The second shape starts from the second note in the major scale. So if you played that one from the D on the 10th fret of the 6th string, you would play the notes D E F G A B D E F G… you get the idea.

The diagrams go on to show you fingerings starting from the 3rd, 4th, 5th, 6th, and 7th notes in the scale.

You can also associate these shapes with the different modes. It’s important to know how the modes relate to each other. Dorian is the 2nd mode of the major scale, Phrygian is the 3rd mode, Lydian is the 4th, etc.

HOWEVER as I pointed out earlier, it is erroneous to simply say that modes are any scale starting from a note other than the root. I don’t know how many times I’ve heard a guitarist say something like “Oh, it’s in C major, but I did the solo in F Lydian”

…NO! You did not! You may have been using a shape that you have associated with F Lydian, but you were still playing C major. If you had really been playing F Lydian, it would have sounded awful. You would have really been leaning on that F note, which would clash horribly with the tonic triad (the C major chord).

So don’t get caught in that trap! It’s not where you start from, it’s all about the tonic!