They are asylum seekers because they seek asylum, it purely comes down to that - the request.
They may be asylum seeking terrorists, asylum seeking welfare sponges, asylum seeking people smugglers intent on setting up a branch on the mainland, asylum seeking middle class professionals looking to upgrade to the first world lifestyle etc - and in all cases they are, just the same, asylum seekers
They may have their request for asylum refused and they were still, for the duration of the processing period, asylum seekers because they sought asylum.
