Greeks would be very offended at that time if someone called them Turks. They fought against Turks for their independence in 1821-1832 and in Crimean war they still hated Turks very much, so these volunteers even wore their national clothes, so the Turks will know that they are Greeks (Russian command not once ordered them to change their clothes for Russian uniform, but they always refused).
But yes, among Greeks in this Legion there were Bulgarians and Albanians too, who also hated Ottomans at that time and wanted to fight them.