The world of Jazz music is dominated by chord extensions. Those are scale tones higher than the fifth scale degree. Any chord chart you read in this genre is going to be at least a 7th form if not a 9th, 11th or even 13th. Very rarely would you play a plain major or minor shape in a this kind of setting, although it does happen.
To start visualizing the extended shapes, start with your basic "Oklahoma" D Major open shape. From low to high, you have the notes D, A, D, F#. Notice that you are duplicating the note D with the open D string and the D on the B string. With extended sounds, you are going to richen up your forms with a little more color.
Next, drop that D on the B string down to C#. This creates a Dmaj7 chord. Now you have a much richer sounding chord with no repeated notes.
So, now you have the essential notes that define D Major 7. The notes are: D, F#, A, C#. If you lower the C# on the B string down to a C natural you now have a D7 (dominant) chord.
This is a key to finding all of your extended sounds. Just take your familiar chords like C Major, for example, and just lower the high C note down to a B note and you now have a C Major 7.
Back to the D7 (dominant) shape you played earlier. Lower the C note on the B string down one step to the open B note. You now have a D sixth form. So you see you can quickly access several different extended forms just by lowering the root note on already familiar shapes.
Good luck with this and next time we will talk about adding 9ths, 11ths, and 13ths into your vocabulary.