Yes, the results are exactly the same. The download version of LanguageTool does not contact any server on the internet. When the option “run as server” is enabled in the options window, you can use LanguageTool via http (see LanguageTool HTTP API). For instance, you can type “http://localhost:8081/?language=en&text=An+test” in the address bar of your browser, and you’ll receive an answer from the (local) LanguageTool server.