The answer is really it depends.
You can set your wall in various ways. The default is that any friends of the person you are writing to can see their wall. Just as any of your friends can see your wall (and everything anyone writes on it)
I think on the home page you'll only see wall-to-wall posts if you are friends with BOTH people.
But again, these are the defaults.
I have my wall postings set so that they only go on the home page of the person I'm posting to instead of to all our mutual friend's home pages.
My wall is visible to all my friends but that is a setting you can change. It is either all or nothing (for each friend) they can either see your entire wall or they can't. It takes some effort but you can set that per person using friend lists and permissions.