What's the difference between Home Sharing and Family Sharing?

I bought a new iMac yesterday. I discovered I already had 5 computers authorized when I tried to set this one up. I ended up deauthorizing my MacBook Pro, which I'm going to give to my kid once I finish transferring data, in order to authorize the new Mac.

How do I find out which other Macs my Apple ID is on? Is there any other way aside from deauthorize all to clear out the computers I no longer use? What's the difference between Home Sharing and Family Sharing anyway?

Thanks,

Shawn