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I'll risk answering the question, though it's probably not gonna be a complete and legitimate answer.I think that the misunderstanding that you have comes from a body of terms and their "historical plaque"What you call static and dynamic servers is usually called static content and dynamic content.What's in the text called the application servers is just like a Web server with no face, no matter how rude it sounds. It's a program that accepts HTTP queries and HTTP responds. Usually called REST - protocol (Representational state transfer)Another common term for "application servers" is Web service.Does API always work with the application server?The term "several apps" itself is a historical silk.I'll explain my thought. At the stage of the WEB's discovery, it's possible to write a file with hyperlinks and to give it to a primitive type browser. https://ru.wikipedia.org/wiki/NCSA_Mosaic It's all right.But I wanted a dynamics, like a customer on the page. It was used. https://ru.wikipedia.org/wiki/CGI (Common Gateway Interface).In fact, it meant that, in response to a request from the browser, a programme would be implemented on the server and the result would be shown in the browser.To "good sell" this opportunity, and the web server wasn'tt just free open source, but sometimes it's very expensive, https://ru.wikipedia.org/wiki/Internet_Information_Services and https://ru.wikipedia.org/wiki/WebSphere - was invented marketing term "Server of apps."Which meant no less than the ability, in response to the user ' s request, to fulfil a code that would respond. That's the difference with the server that can only get the files.Further, the API should probably mean "interaction on a pre-agreed protocol", but for HTTP servers, 99% of the cases should be read as REST API.What is this?I'll give you an example. Let me have a database of valuable information.I can make a web server who's on his pages showing this information on the user's request.I can provide an interface to my database, and many Internet servers will start showing that information on their pages, asking for information to me. API. I may not even have a Web server that has visitors' page.I hope I could, in this short answer, help you understand the terms. But if there's any specific questions, write!SupplementI reread your question, and I decided to add a little to the answer in which part:The application server may contain web servers, so it is considered more powerful than a web server.Here, I probably don't understand the very design or structure of this application server. For what and how does it contain this web server?I'll try to tell you what it means. Let's see what's in all these servers.There's a program that runs HTTP, a protocol. She just knows how to get a HTTP request and there's a module in it. Trying. I'm sorry.Usually this program is just tied to the WEB-server file system, and the "response mode" is working on this algorithm: "Do you have a request? See if there's a file on the CD that matches the request. If there is, give this file back on request, if not, show a page with a 404th mistake." It's what's called "static content," or "statistical server" (however it turned me away from this term)What's a dynamic server? It's when the "response mode" in the program that serves the queries, learns another trick: "...and if there's a certain kind of request to the Web, then instead of the value of the file to the user, do this program, and give it to the user.That's exactly what "The Sever of Annexes can contain web servers" means that, to accept the request and send the answer, we need a HTTP protocol module, and they call it "web server." In this sense, the Dynamic server will collect the Web server in its composition.