Or are they just synonyms that mean the same
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I’m not anti lawn. They are nice for a lot of reasons, but how and why did it become a “thing” to be a small time grass farmer? Is there a historical readon or do people just like it?
This depends a lot on where you are. In North America, it's assumed that a house is free-standing and has a yard.
In the UK, however, I don't think that's necessarily the case, since I've been told that "house" means row-house.
I think this is a cultural/architectural thing which is, one might say, untranslatable in the way you want.
In Modern European architecture, most family homes ('houses') do not include a courtyard. In fact they are very rare. Also, houses that do have courtyards do not have a special name for such a house, they are simply houses with courtyards. Such a house is remarkable for its uncommonness, but is not considered a concept on its own.
It seems you are looking for a single English word for this concept. I note that the Persian for this concept, خانه های حیاط, ( khaneh hayeh heeyat), is most literally three words, 'house', 'with', and 'yard'. So even in Persian culture, where houses very commonly have courtyards (an interior yard), it takes three words. As extensive as English vocabulary is, there is no necessity that every concept possible has a single word for it, moreso when there's hardly a cultural pattern for it.