I found the answer why I only see MapServer:
When you look at your GIS server as an administrator, you'll only see one service, a map service with the Feature Access capability enabled. However when you look at the GIS server as a consumer of the service, for example when you are developing a web app with the service, you will see two ways that you can access the service.
So, I know I'm in the right place and I should now see the 'Update Defintion', option according to above documentation, but it's not there for me.
I need to find 'Update Definition' it in order to modify the name on one of the layers.
This is what I have at the bottom of the page: