I am from Germany, ALDI is from Germany, so I will give you a few basics to interpret because there is no sense to compare items on different sides of the Atlantik ;)
ALDI is from Germany, created by 2 brothers who have divided Germany into ALDI North and ALDI South. Aldi S is considered the better one.
Aldi is the self-proclaimed cheapest discounter.
The basic priciple is to have a low number of different products of the same type, but a relatively diverse range of items. So you can buy a dozen different cheeses, but only one or two brands each.
They also have a low number of workers (btw: No one here in Germany packs the bags for the customer, its all "self-service" ) and everything is optimized for price, location, size etc. That included, as someone has mentioned "Unlike grocery stores that actually have shelves, everything at Aldi is still in the large cardboard boxes it's shipped in." - It just takes a lot more time to put 20 items on the shelf then a single cardboard box.
The quality is on average quite good, meaning you will seldom find anything bad, but even less often something top. That even is correct for electronics.
(btw: If you find a LIDL, it is the same principle, but Lidl is just trying to change their image from cheap to something else, so it may be the cheap variant will never exist in the US.)
I am a bit confused about your reports of the difference in the different Aldi stores. Here in Germany Aldi makes the low prices with buying huge quantitites and dictate prices this way (not to the amusement of the producers). Maybe they are not big enough for that in the US or it depends more on the single local manager (I think I did read Aldi in the US is going more the franchise way; if this is true, that would be the result I think). I dont think it is the difference between Aldi Noth and South, because i think they have split the countries so only one of them in the USA, buy maybe you could ask? I woudl really like to know it, just out of curiosity.
So, at last, from a german point:
I mostly buy potato chips, one sort of cheese, one sort of chocolade and one other sweet item there. Nearly everthing else is from Kaufland 100m away, partly beause if I go to Kaufland anyway I buy the things I coudl buy at Aldi there, too. The price fight especially here is so extreme it is either the same price for brand ware, generic items like milk and flour where there is no difference at all between brands (so take the cheapest) or store-brand anyway, so you cant change. I often joke I only buy sweets at Aldi ;)
I would not recommend the bread there, but that is because it is pre-made like in every discounter and supermarket here, and my local Aldi seems to be not able to manage to keep its assortment stuffed anyway. There are always only half of the bread sorts there when I go in.
I often think of Aldi as a sort of single-market: You get everything you need, but no fancy stuff or wide choice. One size fits all. Go in, grab it, run out.
