"so is Taiwan similar to Scotland is to the UK? Part of it with its own separate parliament? ... Somebody explain it..."
No: the analogy is more with say Juan Guaido & chums being the actual government of Venezuela.
Taiwan claimed to represent China and indeed held China's seat at the UN for many years after the Revolution. It maintained the position until 1971 when a rapprochement with the CCP took place: just before Tricky Dicky's visit to China the next year.