The pentatonic boxes and the CAGED shape are basically the same.
The pentatonic scales have (as the name suggests) 5 notes, whilst the full diatonic scales have 7 notes. The pentatonic scales are the 7 note scales with 2 notes missing. Here are the E-shaped major pentatonic (normally called “box 1” or “pattern 1”) and full major scales and, for completeness, the E-shape barre chord diagrams:
Observe that the notes in the pentatonic scale are all in the major scale. The red dots in the major scale diagram show the notes which are missing from the major pentatonic. There are two notes in each full octave scale. There’s 4 red notes in the middle diagram because the scale pattern covers two octaves.
As I said, this is an E-shape pattern. This corresponds to the E in CAGED.
For each of the other shapes, there are corresponding diagrams.
All the CAGED patterns are movable so you can play them on any root note. Justin shows the pentatonic scales with an A root note in those lessons, but you can move them to any root note you like.
Also, in the lessons you linked, Justin is describing the minor pentatonic and I am describing the major pentatonic, scale and chords. I didn’t use the minor versions in my description because it’s a little more difficult to explain, and you are more likely to be familiar with major chords, but it applies the same to minor keys.
There is a very strong relationship between major and minor in music as you will eventually discover, but that’s a whole different topic. As a bit of foreshadowing, the notes in minor pentatonic box 2 are the same as major pentatonic box 1 (the diagram above). For reference, here’s Justin’s lesson on Major pentatonics:
You need to understand the relationship between chords, and keys and scales. If you are following the Beginners course, Justin has a lesson on this at Grade 3:
In a nutshell, if you know the key and which scale to use, you can play notes within that scale and it will sound good. And knowing the CAGED shapes for the scales you are playing make it relatively easy to switch between major and pentatonic scales, and also arpeggios (which, basically, are chord tones).