auto-negotiation is a connection setting that will automatically adjust to whatever the media speed is that you are connecting too (half duplex or full duplex). I'm pretty sure you wouldn't be using 1000Base in a home network or even a work network unless you work for a really large company.
The 1000Base-T implies that you are connecting to a cat6e network running at 1000mb/s
the 1000Base-X implies that you are connecting to a fiber network running at 1000mb/s
in each of these you would be in full duplex operation so autonegotiation isn't a big deal.