Major and minor pentatonic share the exact same notes -- they are just viewed from different starting points. This is the relative major/minor relationship, and understanding it means every shape you learn pulls double duty.
Same Notes, Different Root
C major pentatonic: C, D, E, G, A. A minor pentatonic: A, C, D, E, G. Those are the same five pitches. The only difference is which note your ear treats as home.
The rule: any major pentatonic uses the same notes as the minor pentatonic a minor third (3 frets) below. C major = A minor. G major = E minor. D major = B minor.
On the Fretboard
C Major Pentatonic (root at fret 8)
Root notes (red) are C. The shape anchors at fret 8 on the E string.
A Minor Pentatonic (root at fret 5)
Now the same notes with A as root. Root (red) at fret 5 on the E string.
Same pitches - C, D, E, G, A - with a different note highlighted as root. When you think "C major," your ear gravitates toward C as home. Think "A minor" and you naturally resolve to A instead. The fretboard pattern does not move; only the musical context changes.
The Practical Payoff
Every minor pentatonic shape you already know is also a major pentatonic shape for a different key. If someone asks you to play G major pentatonic, you can use the E minor pentatonic box at fret 0 - same notes, different emphasis.
The formula: major root + 3 frets = relative minor root. In practice, you often do not move your hand at all - you just shift which note you resolve to.
Practice
Exercise 1: Same Shape, Different Root
Play the box at fret 5 and improvise, resolving your phrases to A for a minor feel. Then, using the same notes, resolve to C at fret 8 for a major feel. Notice how the mood shifts even though your hand stays in the same position.
Exercise 2: Name the Relative
Pick a key - say D major pentatonic. The relative minor is B minor, 3 frets below. Both use D, E, F#, A, B. Practice naming these pairs until it becomes automatic: F major = D minor, Bb major = G minor, E major = C# minor.