Actually, Studio One natively only has Forward/Rewind Bar commands, which forward/rewind TO the nearest bar. The Forward/Rewind Frame/Beat/Grid commands are a part of the Navigation Essentials script and forward/rewind BY frame/beat/grid respectively. Hence the behavioral difference between them.
Though not ideal, but a workaround to combat this issue that I use is to first forward/rewind to the nearest bar and then execute the forward/rewind frame/beat/grid commands, so that they forward/rewind TO the nearest frame/beat/grid respectively.