The use of the apostrophe is equivalent in these phrases?

Question

This is the house of John / This is John's house

Are they equivalent?

Answer 1

I think it's about what is more important to you, is it the house or John? The focus of the first sentence is on the "house", we can just say "it's the house" or "it's the right house" The focus of the other sentence is on "John" since his name came before the house and followed by the 's which may be there to tell us that John is the important thing here so the scope is on John, not the house itself.

Answer 2

As per my comment above, your two sentences are equivalent. They both mean This is the house in which John lives. Ordinarily though, English speakers would say, This is John's house, not This is the house of John. John may or may not own the house, e.g., John may be a kid or just someone who happens to be living in the house.

Answer 3

Although often treated the same, they are not identical.

Consider this example:

？ This is the house of fun.

→ ✘ This is fun's house.
→ ✔ This is the fun house.

In that sentence, fun doesn't own the house, but it is associated with it.

Using of assigns the noun an attribute, but it doesn't ascribe actual possession to it.

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Other examples involving of that mean association with something rather than the possession of it include the following:

That's the bridge of roses.
It was the dark of night.
That's just a pack of lies.
The Barber of Seville.

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To be explicit about possession, equivalent versions of the sentence in the question would be as follows:

This is John's house.

→ ✔ This is the house belonging to John.   OR
→ ✔ This is the house owned by John.

Note that something belonging to somebody and something owned be somebody are subtly different.

I rent an apartment, but I don't own it. It's just that it belongs to me. Similarly, a house can belong to an entire family, but only certain people's names will appear on the deed.

The possessive, on its own, doesn't distinguish between ownership and belonging. That needs to be established by context. However, that's something different.

In some cases, and by common assumption, X of Y means Y's X, but it certainly doesn't have to, and some particular contexts make it clear that there's a difference.