Do you mean store specific? Or that has icons for all the items?

If you just mean written lists, any app that allows you to have several lists open at once would work, even the built in Notes app (that's what I mostly use). In Notes, create a note for each store and select that note to add an item to the list. If you want something of the sort, but more powerful, look under Productivity and Organization. Maybe something like Listaway or Evernote. The basic Reminders app lets you share your lists through the cloud.

If you want to share lists with a partner, AnyList is a good choice. I'm pretty sure it allows multiple lists, but I think you could also use customized subheaders for the different stores. I haven't looked at it recently. It has organization by department within a list, with autofile, and does some high level tricks like recipe import. "Groceries" app is a little clunkier, but for sure does multiple lists, and has autofile and autocomplete, but I don't know if those will work on the hardware, et al.

Pushpins includes offers from major stores.

I used to have a great app for this that was for entertaining, but I can't remember the name, and I don't have my phone to look it up.

There are errands managers. Errands To-Do List would work, but I think it's clunky, and I'd rather just use Notes, but it's the best one I've seen in this category.

Some of the above also let you scan bar codes, but I find spelling it out is easier.

I got Amazon Echo when it was first out to see if my folks would like it. It's not all that useful, really, but what I like enough to keep using it is that it has a shopping list function. You can be up to your elbows cooking, and tell it to put something on the shopping list. The list can be accessed from your phone or tablet (Fire or Apple, I think). It's just one list, but like having a kid around to write it down. :) It will also read back the list. :)

I know lots of people use and love Evernote

Evernote

Zenbe Lists

I am trying to find something like Zenbe Lists which no longer exists. One click and you can see all your shopping lists on one screen (until the list gets too long.) That makes it easy to add things to several lists from this screen. Do any of the apps you mentioned do that? Here is a look at Zenbe, it was perfect for my purposes.

Alternative to zenbe

I love Out Of Milk

My favorite grocery app is Grocery Shopping List. Mind you, I don't have an iPhone, but I use this on my Kindle and on my Samsung smart phone. I am able to have a collection of different groceries/supermarkets, and what I prefer to buy in each. (You can even adapt this to other purchases in other stores not related to food, or online. For instance, yearly gardening supplies.) THe app may well be iPhone friendly, as a lot of them seem to be these days.

My favorite list maker is SplashShopper by SplashData.

Evernote!