Parallel to jHolmes write-up also Finnish baseball (pesäpallo) has its home base but this node is not about pesäpallo, which is, btw, much more interesting game than its American counterpart.

I lived in small village far from everything -- and it was even far from Everything at those days of 80's (which we all should forget, at least the music) -- and we the hay-hats had definitely our own slang.

Home-home refers to home where my parents live/lived. Nowadays I make a separation between my current, hmm, home -- I don't really have one because I'm on the move all the time -- and the home where I grew up.
So, home-home should be defined as a place where you spent most of your childhood and your parents still live there. The latter is not necessary option..