It is acceleration, change in direction in this case, which makes the difference as does the fact that graviton all attraction is a non-contact force.
In space away from any large mass going at 1000m/hr in a straight line does not require a force to be acting on you.
When you go around a corner it is a localised contact force that provides your centripetal acceleration. Your body "feels" the effect/position of that localised force.
For example you feel the effect of the seat and seatbelt in the car pulling on you and the forces involved are contact forces.
When orbiting the gravitation attraction of the Earth provides the force for both you and the spacecraft of just the right amount so that no contact forces are needed for you to go "around the corner". So you do not directly feel by contact the force which is causing your centripetal acceleration.
The idea of having artificial gravity in a space station by rotating the space station would work because you would need an extra force to rotate with the space station and that would be because there would have to be a contact force between you and the space station, a force from the space station which pushes you towards the centre of rotation and you would feel it as an identifiable localised force.
As for the g-forces. In a space station even though the speed is very large so is the radius and thus the accelerations involved are less than 1$\times g$ and vary hardly at all across the expanse of the space station.