I had my texts stolen by another, much newer website and sometimes Google ranks their pages with the stolen text of mine higher... Takes a LOT of time to fight that kind of abuse and sometimes some hosts are just ignorant. And Google sometimes refuses DMCA of my stolen texts even that they host the thief's website at their own Google Cloud servers... Thus I lost interest in creating interesting, quality content for the internet.

Duplicate content is content which is available on multiple URLs on the web. Because more than one URL shows the same content, search engines don't know which URL to list higher in the search results. Therefore they might rank both URLs lower and give preference to other webpages.

P.S. Sometimes I have customer writing they were unable to place an order on one of the two stores that I have on the same website (with an entire page explaining how to use both stores and why I have two stores), so I would direct the customer to the other store and they would successfully be able to place their order. If I had just one store, I would be losing that sale. The two stores are: one is older and another is newer versions and have somehow different functionality, yet the same assortment of goods. Other search engines don't see to have a problem with me having two stores, but on a Google's whim if I delete one of the stores I won't be able to recover it later and what if nothing changes with Google SEO once I delete the older version of the store. Now if I close one of the stores and keep it there, Google still is able to detect it and still may give me a duplicate content "penalty". Imagine even if a single store is selling many identical items that vary only by colour etc. and their text descriptions may be similar to each other. Would that be penalized for duplicate content? There seems that Google must do their homework properly and not push webmasters on their whim.

If I close the second shop to business (disable), will Google still pick it up as duplicate content? I had a third shop on the same domain that I keep disabled for a while and Google seem to have picked it up and reported to me via webmaster central. If I remove the second shop and redirect all those pages, it will take tens of thousands of redirects. Yet descriptions of goods in online stores should not be treated by search engines as duplicate content?

Subdomains are generally treated as a separate sites.

There is no point to run this kind of backup. You can turn the other one off and just keep it on your server in case you need it in the future. Running both at the same time however causes exactly what you're concerned about (duplicate content) which could be bad for both sites. Some role can also play customer confusion, as the sites are living on the same root domain but they look different so where should I order from? What kind of scam is that?

Get rid of one (keep it in the background, backup on your local computer... whatever works for you), redirect those URLs to the other one and your store should do better in search eventually.

Would having two almost identical book stores on the same (sub)domain create duplicate contents problem? I will explain in more detail, so that I can receive a better answer.

Let's say I own a shop on a Mydomain.com (root location) and then I also have an older but also secure and almost identical shop.mydomain.com at the subdomain which is an older version but has the same identical goods and text descriptions in it. Thus:

mydomain.com

shop.mydomain.com

Why have I done that? The older shop has a lot of money invested in customizations and software etc and is like a back up in case if one shop fails I can keep on running a business instead of closing down for long lasting repairs.

Would that create Google's duplicate content penalty?

Same problem with my website as well. I have dumped Google and am using Duck, Bing etc. but not Google. Google are arrogant, dismissive and ignorant. They do not deserve to be #1. Their search is trash.