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   A third chord is a root tone and its third which can be either minor or major, This is the 'other' power chord where most call it what it would be with an added fifth so (C E x ) would be C major and (E G x) would be E minor...

   A C major chord is (C E G) and a C power chord is (C x G) so the third chord would be (C E x), The power chord takes a triad (1 3 5) and removes the 3rd where this one takes the triad (1 3 5) and removes the 5...

   The power chord (1 5) creates 'two shapes' where the VII. position of a key uses one shape and the other six use another shape, Using the bottom two strings you can build the power(5) chord going down or up...

B5 - C5 - D5 - E5 - F5 - G5 - A5 - B5 - C5

NOTE: the 5th of "B dim." is 'flattened' compared to the other six chords...

E5 - F5 - G5 - A5 - B5 - C5 - D5 - E5 - F5 - G5

This shows the building of power chords from the sixth string up to the fifth string...

   The third chord also uses two shapes but the Major positions of a key (I. IV. V.) use one shape and the Minor and diminished (II. III. VI. VII.) use another shape, IT's harder to build these chords up because of the wider intervals so building them down ^^^ is best...

C E x - F A x - G B x - C E x... (major third)

D F x - E G x - A C x - B D x - D F x... (minor third)

   Saying the (E G x) chord is an E minor (E G B) when in fact it could be an E dim. (E G Bb) chord, In theory this would be called a diminished third but the interval is the same as the minor third...

When you extend the third chords then you run into naming problems...

C E x B - - > E sus6
C E x D - - > C major 11th --> ???
C E x F - - > F sus7
C E x A - - > A minor

D F x C - - > F sus6
D F x E - - > D minor 11th --> ???
D F x G - - > G sus7
D F x B - - > B dim.

   Adding the 9ths to the 'major or minor third' is the only one that creates something unique, There are however very sparse on the guitar meaning its hard to build them...

C D E - E C D...    (C E x x D)...    C major 9th with no 5th...

   The first chord shown is super duper hard to play but you could slide the shape down and use an open string, If you slide all three tones down to the next note then you come up with B C D (or B D x x C)... B dim. 9th with no 5...