From the general gist of your question, I suspect you're confusing Amin with Amaj. TMK Lisa doesn't introduce a two finger 'simple Amaj' in her early fundamentals simple chords lessons?

So in that case I'll deal with your question as if an inquiry about 'simple Am' vs Am.

Short version. Simple A minor in that fundamentals lesson is a 'cheat' intended to facilitate early chord changing for absolute beginners as an exercise by providing couple of rudimentary very easy chords to do it with. Simple Am in the lesson requires muting of (i.e. don't play) the top three strings when played. Just don't play them. Technically it is still Am, but not how it is ordinarily fingered by convention, and has a different timbre.

You will learn later to play Open Am differently. Just go with simple Am for now unless you can already finger Open Am conventionally with three fingers, in which case it's fine to use it instead if you want to.

Longer version. Chords are triads consisting of three notes minimum. In the case of a minor chord, those are by convention the 1st, minor 3rd and perfect 5th. Don't worry about how that's all worked out for now other than to understand that in the case of Am that means it must consist of the three notes A, C & E. Ordinarily when we finger Open A minor using the nut as our barre, we use three fingers, using an extra finger so we can fret the 4th string at the 2nd fret for the E note. We use the other two to finger the same strings as used in simple Am cheat for A & C notes. However..., the placement of fingers on the three strings for a three fingered Am is different. But don't worry about that for now either. It'll all make perfect sense when you come to the time to learn it.

"Simple" Am

Because -albeit an octave higher, the open 1st string is an E note, we can cheat by just fretting with two fingers for the A & C notes which still gives us the three required notes A, C, E. But because we aren't fretting the 4th string at the second fret to give us an E note, that open 4th string is a D note so it needs to remain mute which in order to do so we also avoid striking the open 5th string A.

Both fingerings are an Open Am chord technically.

I think I got that all right in trying to KIS whilst still explaining it. 🤔 NVM, someone will point out and correct me if I didn't.

Cheers 😎

Edit: Couple of minor rewording edits for clarity - hopefully.