Trouble understanding the whole OSGi web eco system
OSGi is a standard in terms of API and packaging for interacting software modules. This is similar to other API standards like JPA or Java EE.
An OSGi runtime is a server which follows the OSGi standard, it is an implementation of the standard. You mention some common ones: Knopflerfish, Eqinox. These let you run OSGi bundles.
A web container usually refers to an implementation of the web-specific parts of Java EE (servlets). The servlet standard also defines an API and packaging, just like OSGi, only different.
You need a server to run your Java EE web apps. You package your app as a Java Web Archive (WAR), and ask your application server to start it. There are several servers, as you mention, like Tomcat, Jetty, but also bigger servers which cover larger parts of the Java EE standard, like Glassfish and JBoss.
A web extender tries to unify the servlet standard with OSGi. By adding some OSGi-specific data to your already packaged WAR, the WAR will be automatically parsed and started by your OSGi runtime. Your WAR servlets will be published to the OSGi http service by the web extender. With a web extender, you can run both standard OSGi applications as well as WARs using only a OSGi runtime, without the need for a Java EE-compliant server like Tomcat.
Jens,
As I have some experience with OSGi, I really would not suggest you start with plain OSGi.
Start with Eclipse RCP (Rich Client Platform) instead.
You not only get a OSGi runtime, but a full-featured integrated IDE if you download Eclipse IDE for RCP and RAP Developers edition here.
Lucky for us all, you can get the book Eclipse Rich Client Platform (2nd Edition) which was recently released only a few months ago and contains updated info/guide on Eclipse RCP.
OSGi is the fundamental building blocks of Eclipse RCP, however OSGi by itself is confusing and boring (at least for starters). Getting up to speed on Eclipse RCP is much easier and enjoyable, you can build a functional "do-something" app within hours.
With plain OSGi, you'd already be lucky if you can get rid of ClassNotFound exceptions within the first few days.
After some time with Eclipse RCP, "convert" your app to Eclipse RAP to run it as a web application on a Java servlet container. See if you like it, even if you don't... by this time you'd have already grasped the OSGi concepts & practices that your sailing to "plain OSGi" would be somewhat smoother than if you had started from scratch.
Good luck Jens!
P.S. I also write about this stuff on my Java EE blog, though not always specifically on OSGi.