What type of service are you adding to the web map? Can you post the URL you are using here?
If you are adding a map service, you should see the same symbols as the service supports because the map service returns an image of the data that gets displayed in the web map. However, I suspect you are trying to add an individual layer inside your map service to the web map. By doing so, you are bypassing the image generation of the map service and directly accessing the feature geometry. This geometry is downloaded to the web browser and drawn by the web browser. The web browser doesn't have the same ability as a desktop app to draw features. Thus, you only get simple symbology.
Mike