A Cypriot can only be what ever GR or Oracle defines it as
A better question would be to define a GC and TC independently then just for the fun of it compare any similarities, if any
"Cypriotness" has many diverse and colourful characteristics influenced by many civilisations from the Romans, Hellenes, Ottomans, British, etc. A combination and acceptance of these cultures which moulds "us" is what I suppose some would call a "Cypriot".
In another generation or two you will be able to accept the "settlers" as Cypriots too and love them like one of your own