A single zone system is composed of an outdoor unit, condenser, and an indoor unit, evaporator. In other words, a single indoor unit will cool or heat your home. There are many options for the indoor unit such as wallmount, ductable, cassette etc. The advantages of such a system is that it’s relatively simple to install and budget friendly. It is suitable for open areas small or large, but is less suitable for multiple levels for example.
A multi-zone system is composed of an outdoor unit and multiple indoor units. More expensive and sometimes more complex to install than a single zone system, it is however a more flexible system that allows independent control of each room for greater comfort and reduced energy costs.
Choosing one of these options depends on the configuration of your home but also your needs, your expectations and of course your budget.