In the two situations, the astronauts feel "weightless" and are "floating" in the same way. However the two situations are very much different in terms of forces and acceleration. How can we explain that?
Welcome to SE, and excellent first question!
Your question is very much along the lines of what led Einstein to the equivalence principle, except that there were not any astronauts or space stations in his day, so his feat of imagination was all the more impressive. What he and you realized is that, on a small scale like inside the ISS, the force of gravity is indistinguishable from an inertial force (also called a fictitious force or a pseudo force) that arises from using a non-inertial reference frame.
That implies that an inertial frame is one that is in free fall. There is no experiment that the astronauts can perform entirely onboard (meaning without getting information from outside) that will distinguish the two situations. Taking this idea seriously leads to general relativity.
Basically, gravitational forces and inertial forces share the following properties:
- they are proportional to mass
- they can be removed through choice of reference frame
- they cannot be detected with an accelerometer
In particular, the third property explains the astronauts inability to distinguish the two situations. Physical sensations that are normally associated with gravity are, upon closer analysis, actually due to some other force. Like the contact force from the floor or a chair.