garden in the... garden?
So I've reached that part in the Dutch tree where the ever-"enjoyable" misunderstandings between U.S. (/ Canada?) "garden" and U.K. (/ etc.?) "garden" break out.
If I understand the matter correctly (which I have no confidence whatsoever that I do), U.K. "garden" means both "concentrated area of ornamental plants and other landscaping / vegetables" (i.e. U.S. "garden") AND "area of grass, trees, and whatever else in front of or behind a house" (i.e. U.S. "yard").
In the U.S. "I have a garden in my yard" is a perfectly sensible, natural thing to say, as well as reflective of a perfectly common reality. So what would the British equivalent be? I'm assuming it's not "I have a garden in my garden" :)
Britons use "yard" mostly for an open area of ground associated with a building, often used for craft or even industrial purposes. For example, stable yard or Farm yard or even Builders yard. Such spaces are typically hard landscaped and plant free.
A garden is almost always an area associated with a home and includes planting to some degree, though not excluding hard landscape areas.
If yard is used associated with a home, it's almost always plant free For example the archetypal terraced houses of Victorian industrial cities have "no front gardens and small back yards"
If we are fortunate and our garden is large enough to be subdivided into different purposes we might say we have a "vegetable plot" or "Lawns" or "shrubbery" or "wild flower meadow" etc in our garden.
So to answer your direct question a Briton might say
At my new house, I decided to create flower beds in the front garden next to a gravel drive for access and parking, but in the back garden have a patio immediately behind the house with lawns beyond and a vegetable plot at the very end.
Lawns are a British special interest.
In my rural youth 60 years ago, everyone grew vegetables, either in their back garden or a separate allotment. My father had both and used them to feed us and grow cutting flowers for my mother. Once I could walk he created a grassed play area out back for me and my gang, one that grew slowly in size as we got taller. However the front garden (onto the street) was always for show and always included a small lawn that was definitely "no games".
That was a common pattern so the local seed merchant stocked a "pick and mix" array of grass seeds. There were varieties suitable for the display lawn (to be cut in neat stripes with a cylinder mower) and others tough enough the soccer/badminton patch where the kids frolicked.
In the UK, using the words garden and yard can be inter-changeable, e.g; "I've built a new shed in the back-yard. . . " In this context back-yard could be replaced with garden or back-garden. Sometimes, different regions will prefer using one word or the other, so in the north of England people may use the word 'yard', but in the south, garden. Now, I think a good rule of thumb for the UK usage is, if the land at the back of someones house has plants, shrubs, a lawn etc, its a garden; but if it is covered in slabs and is lifeless, its a yard.
We wouldn't say,"I have a garden in the yard." But we would say,"I've turned the yard into a beautiful garden."
I hope this helps, and more importantly makes sense.
'Yard' usually refers to a partially-enclosed paved area, so it would be perfectly sensible for us to say 'I have a yard in my garden'. 'Garden' unadorned usually means any modestly-sized plot adjoining a house. To refer specifically to ornamental plants/landscaping/vegetables we might say flower/rock/water/vegetable/herb/kitchen/etc. garden; as any of these would necessarily be in the garden senso lato it would be redundant to append 'in my garden'.
There is no equivalent, it makes no sense.
A yard is/was an unplanted area at the back of a house (usually a terraced house) which once housed the outside privy, and has space for storage/hanging out washing/where a child can kick a ball around. These are back yards:
A grand dwelling or an inn has a courtyard - again, hard surface.
If you lay it to grass and/or add planting it becomes a garden - even if it's a patio garden.