Thanks for that info :) does puutarha refer specifically to the public/landscaped gardens? Regardless though, this question will get me every time because yard is never used like this in UK, any space at the back of a house is always a garden, regardless of what’s on the ground - I’ve never heard anything else.
You can have a "puutarha" of your own, it doesn't need to be public, but they are usually slightly larger and have lots of greenery, fruit trees, berries and/or herbs etc. (Do try searching for "puutarha", "kattopuutarha", "mökkipuutarha" etc.) A "piha" is any kind of outdoor space attached to a house or building. It can look like a "puutarha", or not at all.
Interesting! In Northern California, a yard is never hard surfaced. Someone's backyard or side yard or front yard are all going to be green. Usually with grass but many of them are actually gardens nowadays (like my backyard, which is actually a garden, but which we still call backyard).