The difference between single zone and multi-zone heating systems is the amount of control they provide to separate rooms.
In single zone heating systems all the radiators on one circuit are controlled together. (If you’ve only got one thermostat at present, then you only have one radiator circuit). You can change the settings to turn the heating on or off, or you can set a specific temperature to be reached. In each case the same setting applies to all your radiators.
Nest Learning Thermostats control single-zone systems. They are smart thermostats and will do far more than a traditional manual thermostat: learning your habits, anticipating your requirements and automatically turning off the heating if you are away. But they still control all the radiators together. You cannot turn down the heating in a room you are not using, while turning it up in a room that you are in.*
Multi-zone heating systems allow you to create different zones in your home and to set different temperatures for them. You can set up these zones as you want, and normally each room would be a separate zone. In this way you can set temperatures for each room separately.
With Honeywell Evohome multi-zone heating system you can define up to 12 zones as standard, which gives you plenty of flexibility. For example you could set guest rooms to be on low temperature most of the time; the master bedroom could be set to be warm overnight and cool during the day; while the living room might be set to be a cosy temperature in the evening. Whenever you want, you can override a setting for any particular room e.g. when guests are using a spare room or when it is particularly cold outside. This ensures constant comfort without wasting heat.
*NOTE: it is possible to install more than one Nest Learning Thermostat in a house there are separate heating circuits e.g. for ground floor and for first floor. In this case we can install one Nest thermostat to replace each existing thermostat. This provides more flexibility but not to the same degree provided by multi-zone heating.
For a fuller explanation of single-zone, multi-zone and your choices if you already have multiple heating circuits (and so multiple thermostats), please read our article “An introduction to smart heating”