In the US (also Canada I believe) a 'garden' is an intensely cultivated plot of land where one grows flowers, vegetables, roses, etc. The exterior part of a residential lot is called a 'yard.' A lawn would never be referred to as a 'garden' or as a part of a garden, however a lawn and a garden might be the components of a yard.
What are the British uses here?
Are both an intensively cultivated plot of land and the exterior part of a residential lot properly called 'garden'?
Would the exterior part of a residential lot ever be called a 'yard'?
Translate into Britspeak: "Follow me into the backyard and I'll show you my garden."