Numbers in the dots are suggested fingerings. Empty strings are muted or not played [most likely muted!].
The guitar chords in A minor are comprised of the chords that are in three forms of the minor: Natural, Harmonic, and Melodic.
Natural minor is the same tone set and key signature as its so-called relative Major. For Am, it's relative Major is the key of C major. The difference is that rather than C being the I chord, Am is the i (minor one chord). Am is the vi in C, and is C's relative minor (relative, natural, and pure - can mean the same thing). This is a tricky and somewhat outdated way of thinking about keys, yet this way of understanding minor keys is still discussed.
For Natural minor, when Am is 'renamed' the tonic (the one chord), all of the other chords are renumbered as well. In reality, A minor is a modification of A Major.
When we play in the Natural minor, it isn't possible to create a strong A minor tonal center. The tones of C Major tonify the tone C and the chord C Major, not the tone A and the chord A minor.
To create A minor as a resting place in our ears, it is necessary to have a leading tone. The leading tone to an A is G#. To get this tone, we raise the 7 from the pure or relative minor. This creates a leaning into A as the tonic. Along with the D, we have the makings (the tritone) of a key center with A being the tonic. This also makes the V chord a Major chord (and a dominant when 7th is added). This is important in harmony. It creates finality and magnetizes the ear to the tonic chord. Thus, the name of this minor mode is harmonic minor. Harmony is more progressive and strong with a leading tone in the mix (and consequently a Major V chord - the middle tone).
For the scale, the gap between the 6th and 7th degress of the harmonic minor produces a very distinct and memorable sound.
The plus sign (+) = augmented = #5.
The '3rd form' of the minor is called Melodic minor (the melody minor - even though both other forms can be used melodically and harmonically as well).
Together the 3 modes or forms create a large family of chords, modes, and sounds that we call the minor key.
The Melodic minor tone group is the Major scale with a flat 3rd.
Above are just the triads. The family expands when we create 7ths and extended chords.
And, keep in mind, there isn't a universal agreement on naming scenarios. In discussions with other musicianers, I've found that typically everyone is right in how they name or compare/parallel chord systems. It is up to each of us to use what makes the most sense.