Southern Rock is all about the guitar, but specifically the blues-rock sound. Musically, alt-country is, well country, though of course there's overlap, especially in the lyrics.
I wouldn't say Southern Rock is tied exclusively to a Southern origin for the band, but there are virtually no Southern Rock bands that came from outside of the South. In the classic period, anyway. I wouldn't call any band that emerged after the mid-80s "Southern Rock", though of course many later bands have strong Southern Rock influences.