Can someone tell me the difference between a coffee made using the "normal" aeropress technique and an "inverted" technique?
The differences are minor, but there are differences. When brewing normally, water begins to drip through the paper filter immediately when poured over the grounds. After stirring I usually have to add more water after the bloom recedes. Inverted, all the water stays with the grounds until you flip it over and start extracting. The extra water added with the normal process is hotter, and I believe will tend to over extract bitter notes more easily, not only because of the higher temperature, but by virtue of the added volume of water passing through the grounds.
Inverted, however, the volume of water is less, and because of that, the temperature of that water will be lowered a bit. You can extract quickly, or wait as long as you want to extract the coffee. Additionally, I have seen it claimed that with the inverted method, oils that will rise to the top of the column will be forced through the filter first and flavor the coffee more than with the regular method where they tend to get trapped in the grounds.
I have gone back and forth but always seem to go back to the inverted method. It provides more control of the variables and for me gives a better flavor, even when using the same beans, same roast, same water temperature. Your mileage may vary of course.
The difference can be scoped purely to the side-effects of how the coffee is extracted. You can make up for most deficiencies from either method, by accommodating for it.
Normal - starts dripping almost immediately, meaning some of the water didn't get a chance to extract.
Inverted - you can let it brew for as long as you want.
Normal - grounds fall to the bottom and create a self-filtering layer. This layer allows for proper pressure/extraction/etc.
Inverted - as you flip and press you may not have allowed enough time for a layer to form and some of the grounds get stuck to the top - solution: after flipping, whirl the water to collect the stuck grounds and then wait a bit before pressing.
Essentially it's not really that Normal vs Inverted affects the taste directly, but rather what you do with that position of the AeroPress is what affects the taste. Having the AeroPress inverted ensures that you are fully submerging the coffee in water which you can now label full immersion brewing. If you allowed the coffee to drain in "normal" orientation, you'd instead be essentially drip brewing at least a small part of the coffee. The effects on the resulting brew could be nominal and undetectable, but if you were to drastically change time/pressure/stirring/agitation/bloom/ratios THAT is when the resulting coffee taste would change.
Check out my blog article for the AeroPress, it explains a lot of how the different AeroPress techniques affect the coffee.
@Jason Abalos has a superb answer here but since I don't have reputation to comment, I'll expand in a separate answer: Inverted is heavily preferred. I suspect that perhaps the risk of topple and therefore burn is the reason the default instructions do not mention this technique. The primary criticism of this technique being lack of formation of a grounds filter during plunging is easily addressed as Jason mentions by just waiting a bit after tilting upright before plunging. To clarify, since timing is a hugely critical part of the Aeropress brew process, I substract 30s from the brew time and allow 30s upright before the plunge. I also recommend using two filters.