Once the shuttle is retired only Russian Soyuz vehicles will carry people up/down. Russian Progress vehicles will also be the prime resupply option other than these HTV vehicles or the ATV (european) ones.
And no, they're not shuttles, calling them that would be silly. Actually the shuttle refers to the entire stack on the ground before launch which includes the external tank and SRBs, once it's in space it's simply called an "orbiter." I think "space ship" is very appropriate for all vehicles, the problem is that the vast majority of people associate "space ships" with alien technology and outrageously cool designs we've seen in sci fi movies, the real things don't look anything like that.
Cheers!