A web server responsibility is to handler HTTP requests from client browsers and respond with HTML response. A web server understands HTTP language and runs on HTTP protocol.
Apache Web Server is kind of a web server and then we have specific containers that can execute servlets and JSPs known as servlet container, for example Tomcat.
Application Servers provide additional features such as Enterprise JavaBeans support, JMS Messaging support, Transaction Management etc. So we can say that Application server is a web server with additional functionalities to help developers with enterprise applications.