I mean, ERE isn't about frugality for the sake of frugality either. ;) (I know, I know, you don't want to focus on ERE. But it's so awesome I might have to anyway. ;) )
Mustachianism, to me, is about re-examining what makes you happy, realising it usually isn't spending on stuff that you barely use, and therefore becoming less dependent on people paying you money in return for wasting your life away on pointless bullshit, so you can therefore do something you actually want to do in your life instead. "Maybe if we have a smaller house we will still actually be happy, and hey, we'll have less to clean! That second-hand car is actually pretty reliable, so we can get rid of this expensive new one, and also we'll stop driving to the store that we could walk or bike to easily. I'm spending an awful lot buying these things that I just shoved in a cupboard to forget about - did I really need to do that? I wonder if a holiday to that cheaper, closer place could be just as fun as flying to the other side of the world?"
Mustachianism only goes so far, though. Generally the typical Mustachian lifestyle still vaguely resembles a middle-class lifestyle, and while there is some encouragement to look at the impact your lifestyle has on the world, that aspect really isn't all that focused on.
ERE takes it further by being willing to think outside the box: "What if we don't actually need to live in a single normal-sized house with no other families living in it? Could we get rid of our car altogether? Can I do this entire DIY project myself, and spend less than usual on the materials too? Can I choose my hobbies deliberately so that they actually save me money over time? If I make friends with my neighbours can I get them to lend me their lawnmower instead of buying my own?" It also encourages a thoughtful, connected lifestyle, where the things you spend time doing are more in line with your goals for your life. Really, though, it still has the same underlying principles as Mustachianism; it's just willing to take them further. The base philosophy is not that different. Actually, I often wonder why so many people who find Mustachianism seem to stop at a certain point and resist so strongly the further examination of what makes them happy.
As for what I'd say to someone at a party, maybe I'd try, "The thing that makes me happiest is more free time, and I don't care about buying things that much, so I'm saving my money so I won't have to work as much in the future."