Once you get where the differences lie it's actually pretty easy. To tease those apart in text we need some good language though, and I don't think the Enneagram literature's language is very good for it, as evidenced by mass confusion over the types. They're trying to get at something real both in that people fitting those descriptions do exist and that there's differences between them, but the way the differences are explained and articulated could stand improvement. A ton of it.
So let's use Big 5 for our little exploration here - the system has a lot of separate traits that can help get to grips with eg. their expression of anger and displeasure in a more nuanced way.
First, let's lay out some general traits that all people have different levels of.
The first trait is Extraversion - it's not just sociability, but is actually based around reward-seeking and covers things such as sociability, assertiveness, activity, warmth and positive emotional response.
The second is Neuroticism - this is a general trait measuring negative emotional responsiveness. That is, if you put a negative signal into the person, what magnitude and kind of response you get. This is more about the person's internal state than how they choose to act upon it. A high negative emotionality person could be absolutely crushed or insanely angry at some negative thing happening while someone low on the trait would experience a resounding "meh". It's how hard events hit you. The positive emotionality part of Extraversion acts the same way. Neuroticism has a bunch of subfactors, but they tend to fall into two camps: Nervous withdrawal and angry hostility.
A third useful trait is Agreeableness. We all have a capability called theory of mind - the ability to represent what's going on in other people's heads in our minds. This includes what they're likely to be thinking, feeling, etc. Agreeableness is a measure of kindliness, of giving a shit about how other people feel. High-Agreeableness people use their theory of mind actively, and actively empathize with other people (Agreeableness is the other trait that drives higher sociability). Low scorers aren't automatically assholes, but while they don't have problems with theory of mind per se, they don't tend to actively consider other people's feelings. It can be an active dislike of others, but often just part obliviousness, part no-care. Agreeableness has been shown to inhibit the expression of hostile feelings (what a surprise there, right?), so a displeased high-Agreeableness person might just swallow their misgivings, while a very low-Agreeableness one would likely just blurt it out.
A small note: Extraversion and Neuroticism cover a person's emotional response - the impact rewarding or negative emotional inputs have on the person, but not eg. their desire to mull over their emotions. A desire to watch sad movies to experience melancholy would fall under an aspect of Openness, not Neuroticism. You could conceivably have a person whose emotionality is near nonexistent and they'd feel driven to contemplate the sheer flatness of it.
Now that we have some language, distinguishing between people we'd call Sixes and people we'd call Eights is pretty easy.
Eights are people who tend to be very high on Extraversion - they're outgoing, reward-seeking, don't have a problem speaking their minds and bossing people around if need be. They enjoy life.
They also tend to be very, very low on Neuroticism. That is, negative signals just don't register as anything very big in an Eight's brain. Makes for a solid, sturdy unbotheredness but they may also just care too little. In this sense, calling Eights a "reactive type" or even particularily angry is very much a misnomer. They are severely underreactive if anything. What Neuroticism they have is likely of the angry hostility variety.
Now, why would Eights have a rep as angry people if they're rarely in an especially negative mood? The answer comes from low Agreeableness. Eights don't care overmuch about how other people feel, and don't terribly actively factor it in to their decisionmaking. The low Neuroticism doesn't help - what might merit a shrug from a low-Neuroticism person could seriously wound a more responsive person. Low Agreeableness means that even if an Eight isn't distressed by negative events, they don't have much of a filter when it comes to expressing their displeasure - even if it isn't much, the situation is still negative so might as well fix it right? So both can be true at the same time - they're telling the truth when they say they don't really feel that angry, but can come off as unnecessarily hostile or as whiny little never-enoughs.
The low Agreeableness also means they have to expend a bit of effort or to consciously build up a habit to keep up with all kinds of side-channel information in social situations since it's not a habit they're naturally drawn to - much easier to be frank and upfront, right? Not like it'd hurt anyone, since like most people they assume people are a lot like they themselves.
Now, contrast with Sixes. The main thing that stands out in Sixes, Big 5 -wise is, by far, Neuroticism. Sixes are defined by a high responsiveness to negative signals. Some react in a panicky way, others are hostile and grumpy, some a mix, but the constant is that the negative-o-meter is trigger happy and the impact big. Sixes are the reactive type par excellence.
The mixed Six population is pretty normal otherwise, they range the gamut on things like Extraversion and Agreeableness, but it's not hard to imagine a counterphobic Six as someone high on Neuroticism with a decidedly hostile lean. Some very irascible individuals might also have low Agreeableness - they're angry, and they don't have a filter. Run for the hills. Others might be angry but be more normally considerate of how other people feel and not end up visibly raging but still clearly very displeased by events when you know what to look for.
In here, we can notice something interesting: Counterphobic Sixes sometimes say they don't really feel afraid, but the Enneagram literature says the explosiveness is a cover over fear. This is probably another case of half true, half not. Both hostility and inhibitory withdrawal correlate with each other, so the angry counterphobic is likely to be more fearful than the average person as well. But it's also conceivable that there are some people who aren't unusually anxious at all - they just have a heightened hostile emotional response.
