As far as I know, for standalone glassfish server case, the context root also needs to be unique. When you deploy an application without specifying a context root explicitly, a default context root will be assigned if none is specified in sun-web.xml. And the default (which is derived from the application name) is probably different for the applications you deployed. Maybe you could provide more details here..
When you say "without context root", did you mean the root context "/"? If you want to specify root context root, you will need to specify context root as "/".
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