Then it became the "International Space Station" (ISS) because we and the Ruskies were going to be BFF. For a considerable period of time the neo-Soviets (excuse me "Russians") had a monopoly on launching personnel to the ISS. Fortunately SpaceX can now do the job and we call tell the neo-Soviets to go pound sand.
NASA and SpaceX Complete Certification of First Human-Rated Commercial Space System
Meanwhile, although they deny it, the legacy US rocket launch crowd United Launch Alliance (Lockheed Martin Space and Boeing Defense, Space & Security) and Northrop Grumman are in trouble because they've been buying rocket engines from the neo-Soviets.
Russian space chief says Russia will no longer sell rocket engines to the US
BFD. We only use(d) Russian engines (The once excellent, but now nearly obsolete RD-180) on the Atlas-V, and then only as a favor to Russia (so their rocket engineers would have something to do other than work for Iran and North Korea). Atlas-V is now semi-retired. No new rockets will be built, and the remaining 22 have all been both built and sold. Russia can keep their engines.
SLS, if it ever launches, will do so with American engines.
The current workhorse for both manned and unmanned launches is the all American (and private sector-ish) Falcon 9.