I think mods is just that, mods and nothing else. a rod, is probably an all out machine that SHOWS its modified, and looks good to boot.
think like a nice classic Bel Air with the big ol tires on the back, nice paintjob, a lovely 454 bigblock under the hood and some performance. in my opinion, this is a rod,
a MOD, to me, is just your essentially stock car, such as say, an earlier mustang with a stock look, and some bolt on stuff under the hood, like cams, heads exhaust, etc