The system for naming the patterns is based on the pentatonic scale degree. Major and minor pentatonic scales are built the following way:
Pattern 1 starts with the root, Pattern 2 starts with the second note of the respective scales, pattern 3 with the third, etc.
The reason your 3rd diagram is named Pattern 1 is that even though the fingering is identical to diagram 1 pattern 5, it is pattern 1 of a minor pentatonic scale where the root note is the first note on the low E string. In diagram 1, a major pentatonic scale, the root note is the second note of the scale, thus it is pattern 5 of the major pentatonic scale. If you play this pattern say on the 5th fret you will have the notes of both an A minor pentatonic AND a C major pentatonic. These two scales and keys are related to each other (relative major and minor), the only difference is the root note.
Another potential confusing thing about these is diagram 1 gives you fingerings with the root note in red but diagram 4 gives you the actual scale degrees, not the fingerings.
I believe the site diagram 3 came from is better because it teaches you scale degrees instead of fingerings so it helps you to actually learn and know what you are playing. You will also discover that all of these fingering patterns work for both a major and minor pentatonic scale that are relative to each other.
Do this for fun, record yourself strumming a C major chord for 8 bars then switch to an Am for 8 bars. Repeat it a few times. Now play along to it and improvise melodies using the same scale (pattern 1 minor/pattern 5 major) starting on the 5th fret. You’ll see that the same scale works equally well over both chords because of the relationship between C major and A minor, their scales have the same notes.