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Delivery at home, at a home, in a home?

I've read an article (see the link below) and there's a sentence which confuses me:

No matter if your delivery takes place in a home or at the hospital...

If I rewrite it this way:

No matter if your delivery takes place at home or in the hospital ...

is it still correct?

And if so, what's the difference between two of them?

sheknows.com/parenting