It's pretty common on earth that people grow food in proximity to their home and where the soil is fertile. It just takes an american to make it into an "Aha" moment, hence the snarky remark about fish and ocean. But there you go.
First, we need to come to a universal understanding of the term "garden". What the UK understands as garden would be considered the back yard in the US. Some people in the US choose to have a garden in their back yard while others do not. So for purposes of discussion, let's call garden the spot where you are actually growing plants for food as opposed to a flower garden.
Is that common with the stated definition? In the US, it is not especially if you add sustaining levels of production vs just hobby level
In the US, garden is the area of the yard that grows plants. It is typically a small portion of the yard. The yard is pretty much any open space of the owner's parcel of land not containing the house or other structures. Also commonly used terms are "flower beds" or "plant beds". These are typically for ornamental plants vs food. Most people would consider a garden to primarily be for food plants.
For example, the Great British Bake-off has the tent in the garden. But no red blooded 'murican would consider that expanse of manicured grass as a garden.
Yeah possibly poor choice of words for an international audience. For non-brits, imagine I just said "additional, nature-y non-covered area of your place of residence".