Is the US Soccer federation just selling teams to play at the International level or does it do other things?
It's hard to explain. They are basically the US FIFA member and run many of the soccer programs in the US.
https://en.wikipedia.org/wiki/United_States_Soccer_Federation
Most professionals play for their club teams most of the season and a few scheduled weeks out of the year the clubs have an "international break" where select players are called up to the national team and play other national teams. These can be friendly matches, or qualifiers for various competitions like the world cup, or the north american cup (the CONCACAF gold cup.) It is considered an honor to be called up to the national team.
For women it's a bit different as there are far fewer professional clubs and they don't make much money. US women players are generally going to be full time club professionals, but some of the teams they play have teachers and store clerks playing too.