A chord is simply a set of notes played simultaneously.
When we are thinking in terms of anchor notation, then we can take these notes and turn them into anchor intervals.
To make this more concrete let's say that our chord was made out of the notes 2* 6* 9* and that our anchor note was 2*, when this is the case then we can re-write our chord using anchor intervals and it ends up looking like 0 4 7.
From here on out when we want to talk about a chord we will have some implied anchor note and then we will write our chord using anchor intervals.
Something that we will learn about is that each chord has a quality to it, a quality is defined as how the chord sounds, and doesn't change when the whole chord is shifted around as long as the gaps between the ai's stay the same.
Even though the pitch of the chord changes in the next example, the underlying structure of the way produced by that chord stays unchanged meaning that it will have a similar effect on the listener.
So for example, the two chords 2 5 9 0 and 4 7 11 2 actually have the same quality since the gaps between the ai's is 3 4 3 in both chords (2 + 3 = 5, 5 + 4 = 9, 9 + 3 = 0 and 4 + 3 = 7, 7 + 4 = 11, 11 + 3 = 2), but just because two chords have the same quality doesn't mean that they have the same effect.
Every chord you play is made up a series of anchored intervals and also has a quality to it, these two properties are the main factors which determine the sound and effect of a chord. Two chords with the same quality but different ai's will sound similar but not the exact same, two chords with the same ai's but different quality will sound similar but not the same.
Working with the ai and quality duality is a skill you will learn over time which is a skill which is less obviously learned using the standard method (it's usually implicity learned).
An inversion or ordering of a chord is a rule which tells us in which octave each of the notes in our chord will live. The reason why this is important is that the lowest note in a chord is the one that has the greatest effect on the listener (we will talk about that later).
Additionally when the notes in a chord are ordered differently then sometimes the quality of the chord can change, for example if we looked at the chord which involves the ai's 0 4 7 11 and played it with lowest note of 7 then we can write it as 7 11 4 0, if we then analyze the quality of this chord by setting our anchor note as the one being represented by 7, then it becomes 0 4 9 5 which has a different quality of 0 4 7 11.
Even though different orderings may create different qualities, these qualities don't actually change by that much, so a lot of the time the inversion or ordering you choose won't modify things too much, and when you're playing in settings where creativity is embraced then your choice of inversion or ordering is usually fine no matter what.
For the context of this course since we have a focus on improvisation and chord construction we will not focus on notation which specifies orderings and instead be able to choose orderings ourself based on the fretboard.