Here's an example of saying the same thing 3 different ways: a) body language - this is a compound noun (noun + noun) b) the language of the body - this is grammatically correct c) the body's language - this is also grammatically correct Regarding example a), compound nouns exist only in some cases. So in your case, "house beauty" and "child heart" are not said. No-one has coined these expression in specific contexts yet. Maybe one day they will. So this means that you should only use compound nouns that you have specifically learnt. Regarding b), this is what you do when you don't know of a compound noun. This always works. But you do risk being unnatural if there is a compound noun (like here, "body language"). But at least, you won't be wrong. Regarding c), the possessive -'s works only in some cases, for example, for people and collective nouns e.g. Fred's book, the group's task. Regarding things, for me, it's less clear when it's natural to use -'s and when you can't. (Anyone else? I'm sure I've seen some rules here but I can't remember) The "child's heart" is good. The "house's beauty" doesn't sound quite so good. I prefer "the beauty of the house". The "tree's branches" is good. The "paper's size" isn't so good. In fact, there is a compound noun "paper size" and you could also say perfectly well "the size of the paper". More to say but this is enough for now!

They pretty much mean the same thing and you can use them interchangeably. Sometimes it just sounds better to use the longer form (i.e. beauty of the house) when the noun ends with an "s" sound. When you add an apostrophe "s" to such a word, it can sound a little awkward.

I agree - they have the same meaning.