The split system is the main type in use today as opposed to a “package” or “all in one unit” which is rarely used except in very rare circumstances due to noise and many other limitations.
Split ducted systems are available in both inverter and fixed speed systems. “Inverter” units have a variable output which is ideal for cooling. “Fixed speed” units are a great choice for both cooling and also where heating is a priority. The modern fixed speed with inverter hybrid systems offer the best of both worlds.