I\'m having trouble undrstanding the difference about both platforms? Both seem to offer an environment for deploying and managing applications. First I thought app servers
There is (to some extend) an overload of the term "application".
OSGi is a runtime environment (and development model) for modular Java applications. The term "application" in this case can be really, really low level. For example, an application server can be considered such an "application".
Application servers are also a runtime environment (and development model) for Java applications. However, the term "application" in this case typically refers to a higher level application type (eg., web applications). Application servers typically include a rich set of higher functionality and programming APIs for building web applications (Servlets), persisting data into databases (JPA) and clustering capabilities. Most application servers these days are composed of modules (eg., core, servlet engine, EJB container, etc.). Some application servers use OSGi under the covers. Others have their own modular runtime environment which also offers OSGi capabilities.
But it's also possible to develop higher level applications (such as web applications) directly using only OSGi runtime environment. However, an OSGi framework itself does not include any of the additional functionality. It has to be assembled yourself. There are some "distributions" that include a framework and several modules.