My understanding is that the British and American meanings for the word garden are different. In the U.S., a house might have a yard, meaning the area of land/earth in front of (front yard), beside (side yard), and/or behind your house (backyard). The yard might have grass, shrubs, flowers, or just dirt and rocks. It might not be pretty and it might not have any plants growing.
I think Brits call the yard a garden. In the U.S., a garden is an area that is cultivated to grow particular vegetables, flowers, fruits, shrubs, etc. It can be decorative--they have many beautiful flowers in their garden--or useful--she grows vegetables and herbs in the garden.
Therefore I have a yard but I don't consider it a garden. I have grass growing in my yard (a lawn) that is kept trimmed, and I have some shrubs in a planting bed that don't get much attention. We trim them occasionally. I don't plant new plants regularly or put in seasonal flowers. So I wouldn't say that I have a garden.
In the U.S. most houses in suburban or rural areas have some kind of yard. Some people pay someone to take care of the grass, like mowing and applying chemicals to control weeds, and maybe trimming shrubs. Some people do the work themselves. Some people have what I would call a garden, with pretty landscaping or vegetables. A lot of people keep this kind of garden because they enjoy gardening as a hobby. Wealthy people might have a gardener who maintains this kind of garden for them.
I hope this helps!