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I've played piano for many years and just started learning guitar.

I've been learning the major 6th chords, but I've noticed that many videos and chord charts don't have any regard for the bass note that I would think of as the root on the piano.

The specific example is that they will say that a chord is a 6th, but it just doesn't sound right at all to me since it is really the minor 7th inversion. It does not sound the same to my ear at all, even though I know they are the same notes.

For example, if I play C E G A, where C is the lowest-pitched note, It has a very different feel to me than if I play A G C E, even though they are the same bundle of notes.

Am I missing something basic about how chords are perceived for guitar, or are there just many sloppy guitarists? If the latter, do I just have to muck around on the web until I find the fingerings that have the correct root?

Unlike other posts I've seen here, it doesn't bother me if there are extra notes, and I know different styles are supposed to be "sloppy" to sound right. I also understand that it can really depend on if you are playing with others (e.g. the bass player supplies the root) or if you are trying to focus on other things like the melody. I just want to fill this gap in my understanding and learn how to supply the root if I'm playing solo.

If I follow your description, you are talking about a chord with tones A C E G.

In modern Roman numeral analysis, in C major that would be...

Root position...

First inversion...

You understand chord roots and inversions and so see the second example as an inversion of vi7 or Am7.

Sometimes the chord is labeled C6 or Cadd6 as a plain C major triad with an added sixth.

That label is popular in jazz and pop music. It also has some historic significance when prior to the theory of chord roots and Roman numeral analysis figured bass would have presented this chord as rooted on C with a perfect fifth and major sixth above the bass.

Importantly the different labeling changes the analysis of harmonic function! In the key of C the first case is a vi chord and with the jazz/pop label it's a tonic I chord. The figured bass would be the equivalent of an inverted chord and definitely not a tonic C chord.

In the above I deliberately compared Am7 as vi6/5 and C6 to highlight the ambiguity when swapping between the different labels. But in reality I would say the commonest classical appearance of the inverted chord is ii6/5 a kind of subdominant rather than a vi. In pop style the add6 chord can often be a decorated tonic I chord.

Am I missing something basic about how chords are perceived for guitar, or are there just many sloppy guitarists?

You may encounter some people who are unaware of analysis by chord inversions, keys, functional harmony, etc. Personally, I would have trouble with lessons from someone who didn't know the various labels and theoretical approaches. But it really depends on the exact content of what is presented. Maybe you can translate some pop things in Roman numeral analysis. If it's a hopeless muddle, look for better material. Plenty of rock/pop musicians know theory.

I've noticed that many videos and chord charts don't have any regard for the bass note that I would think of as the root on the piano.

Bass and root are two different things. They can be the same when a chord is played in root position, but a chord played in an inversion is still the same chord.

they will say that a chord is a 6th, but it just doesn't sound right at all to me since it is really the minor 7th inversion

If the sixth is in the bass it's identical to a minor seventh in root position. But ALL major sixths are some inversion of a minor seventh chord. Whether you call it a sixth or a minor seventh depends on the context, and the inversion to be played is a separate decision.

Chords aren't perceived any differently on the guitar than they are on any other instrument. How they're voiced on the guitar depends on the situation. As a guitarist, if I'm in an ensemble that has a bass player my choice of voicing isn't going to determine the inversion being played, because the bassist is almost certainly going to come in below me - so I will tend to grab the voicing that results in the least motion up or down the fretboard. If I'm in a solo situation the voicing decision might depend on realizing a particular bass line. That could mean playing a root position voicing, but it might not.

If you aim to be a competent guitarist you need to learn how to play chords in every inversion, because there will be times you need a specific one. If you only learn chords in root positions you're going to be doing a lot more work than you need to, because you'll be constantly moving up and down the neck, and you probably won't sound that good... long strings of root position chords become boring.

are there just many sloppy guitarists?

Well, yes, there are. But that's not a consequence of the voicings they choose.

It is like you say. With a bass guitar that plays the root note all would be less complicated. The guitar has six strings. Some tones are doubled and most of the chords appear in an inversion if you play all strings. It depends which pattern you want to choose. You as a pianist will be able to derive any chord pattern of a guitar chord containing exactly those tones you want to have. So you can continue looking around, may be you find the one chord you're looking for or you develop it yourself. The best way is to know which chord you want to transfer from the piano, notate it draw the pattern yourself and you'll know what strings you have to play or not. Ask what is the root of the chord and derive the sixth or seventh chord.