Shapes are indeed interesting. He says there are 4 shapes because you have 4 fingers. He's not 100% correct.

There are four shapes because there are 4 unique strings. Mathematicians know this as Group Theory.

On guitar there are 5 shapes (Google CAGED) because there are 5 unique strings (the 6th string, E, is not unique).

On uke some people try to use the guitar's 5 shapes (Google CAGFD) as a transposition of the guitar's, but they are wrong to - the uke doesn't have the equivalent of the guitar's A string, and the resulting so-called D shape replicates the C shapes.

The tenor guitar is also tuned in fifths, and triad chords are worth looking at (they are more common on violin than using all 4 strings, and they only use 3 shapes). This video is very sweet (I haven't yet found a part 2): - 

Here's what we mean by three shapes on violin (I didn't watch all of the mando video. Sorry if I repeat him)

Let's call (on D A and E strings)

shape 1 = DAF# or DAF (D major and minor with D string as tonic)

shape 2 = DBG or DBbG (G major and minor with E string as tonic)

shape 3 = D#BF# or DBF# (B major and B minor with A string as tonic)

If we use all 4 strings, we have two triads side by side (by dint of the fifths tuning, which guitar and uke don't share): -

E.g. the Bach BWV1001 prelude in G minor - the opening chord is GDBbG.

The GDA strings are shape 1 and the DAE strings are shape 2.

Using all four strings, you'll see there are only four possible shapes: -

1+2

1+3

2+3

3+1

(I mapped all this out years ago in a notebook, but I don't have it any more, so the above is from memory. If I've made any mistakes, I'll edit it). The best thing you can do is map it all out yourself.

That's how to keep grandkids quiet, Emily!

Here's what you say to your grandkids: - "It's music theory or straightjackets and gags. The choice is yours."