Q:

"Bakeshop" vs. "bake shop" vs. "bakery" vs. "bakery shop" vs. "bakehouse" for a baker's shop, and "bakeries" for "baked goods" in AmE

Are all four terms in current use in AmE today to refer to a bakery's shop where bread and other baked stuff like cakes and pastries are sold?
As far as I know, "bakeshop", "bakehouse", and "bakery" can designate also the workplace where the baked goods are made. But "bakery", unlike "bakeshop" and "bakehouse", can additionally
refer to an industrial baking facility, i.e. a baking plant.
Also, can the baked goods [bread, cakes and pastries produced in a bakery] be referred to as "bakery" or "bakeries" in AmE?
Even though the latter is validated by the OED for BrE source, I can't seem to find a US dictionary online that states it as fact for AmE.
http://www.merriam-webster.com/dictionary/bakery
http://www.thefreedictionary.com/bakery
http://dictionary.reference.com/browse/bakery

A:

Generally, in AmE, a bakery is a place where baked goods are made, and usually also sold (though there are some factory bakeries which don't sell retail.)
I have some fond memories of the local bakeries as I was growing up. Somehow, they seem to have been replaced, but not by bakeshops. I never saw that word until this post. (Similarly, I have never seen bakery store.)
Now it seems quality baked goods are sold in a variety of settings: the bakery section of a grocery store, patisseries, cafés, specialty pastry shops/stores, and sandwich restaurants such as Panera Breads (which bills itself as a "bakery-café fast casual restaurant".) Cakes are often in specialty shops which only do cakes & cupcakes, as well as in the bakery section of stores.
If people use the term "bakehouse", it must be an outmoded or industry term; I have never heard it.
The baked goods are not referred to as "bakery" or "bakeries". Those are the places that make and sell baked goods. Though shops are where people ply their trade (butcher shops, barber/beauty shops, etc., a baker works in a bakery, though I can see how some people might call it a baker's shop. But not hereabouts.
This is from the New England/Mid-Atlantic areas of the US.

A:

I have never heard bakery store or bakeshop used in the US. Google NGrams (of written english) report similarly. When we buy baked goods, we go to the bakery or to that part of the grocery referred to as the bakery (or, in store-clerk speak, just bakery, as in "You want fresh pies? They're over in bakery.")
First, just showing Bakery, US vs GB, they have similar levels of use in both the US and British corpus:

Comparing Bakery, bakery store, bakeshop, bake shop  (US only), it shows very little or no usage of bakery store or bakeshop:

Comparing Bakery, bakery store, bakeshop, bake shop  (GB only), it also shows very little or no usage of bakery store or bakeshop:

While I haven't heard bakeshop very often, cake shop or pastry shop are more common, but still far below bakery in the US literature:

As for your second question, I have never heard what we call baked goods or pastries (a subset of baked goods) referred to simply as bakery the way your british dictionary does. Searching several dictionaries with Onelook.com, only this one (yourdictionary.com) and this one (Oxford Dictionaries) refer to bakery as including baked goods. There were about twenty dictionaries that made no mention of this definition.

