In other words, are these two structures equivalent?
Yes, they are both (S)-2-chlorobutane.
The difference between these structures is a rotation of the molecule by 60 degrees. You could build a model to convince yourself that they are the same. The arrangement of the atoms around the chiral center does matter.
The utility of the R/S convention is that you can unambiguously decide whether the two compounds are the same or different, which can be difficult depending on the orientation of the compound.