Literally the same groups, it's just that they've been put into their own branch like how the Air Force was split off from the Army after WW2. Mostly just means that they aren't stuck playing second fiddle to entrenched interests in the Air Force.

The Space Force operates the various military satellites. So GPS, military communications, missile warning/tracking, military weather satellites, etc. They also do a lot of work for the National Reconnaissance Office, which is the organization running all of our spy satellites. They search for and track objects in Earth orbit and make the data publicly available. They run space-related military facilities.

So no space battleships (yet, anyways), but they do handle a lot of infrastructure which is invaluable to both the US military and the civilian world.