Both idioms have to do with some sort of physical underlying feature that leads in a certain direction. They both have to do with a particular state of mind. They both also tend to help define how one feels about where they are at a particular moment. However, there are worlds of difference between them once you delve a little deeper.
In the groove may come from following the beaten path. Things are easier when the going is smooth. Some think this comes from pioneers, making their way across the Unites States, following grooves cut out by wagon wheels, making life easier than all the bumps and boulders they would have to endure if there wasn’t already a trail before them.
Another line of thought is that records, old LPs, have grooves. One would place the needle of the record player into the groove, and the music would play. This seems more likely than the pioneer reference because of other groovy terms like getting your groove on and feeling groovy.
Stuck in a rut, on the other hand has nothing groovy about it. This one’s also attributed to pioneers, but not in a good way. The covered wagons were built to haul the settlers’ possessions across the rugged terrain, but with the existing technology of the time, there were some major malfunctions. Axles would snap, tongues would have to be replaced, and the wagon wheels would get suctioned into the mud or slide into the deep ruts made by prior travelers.
Being stuck in a rut means that one feels they are making little headway in whatever endeavor they’re undertaking. This could be the monotony of the day to day. It could be slow progress on a project. In fact, the only cool thing about the phrase, ‘stuck in a rut,’ is that the distance between the left and right wagon wheels became the measurement between the left and right railroad tracks which is still used today. The best part is that, because of how the pioneer wagons were built, this is also the distance between two horse assholes when they’re standing side-by-side!
Thanks for reading!