The system says 'this departure is full'. What does this mean?

You are too late. All seats on this route have been sold already. Try another time/day/mode of transport.
It could also mean that the bus operator has manually reduced the available seats down to zero, because they are sure they will be able to fill their bus with walk-in customers. You might be lucky to still get a ticket at the operator's counter at the bus station.

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Thai Railways

OK

I don't have a booking number. I have not purchased a ticket yet.