What is a groove? Whatever it is - it makes me want to dance. It’s a “feel”. Machines don’t understand “groove”. Humans do. It is the breath in music, the difference between mechanical and wonderful.
It can also be defined as “a situation or an activity that one enjoys or to which one is especially well suited”, for example, you may have found your “groove” in sewing, or teaching. or engineering, or gardening or writing.
What is a rut? It alludes to having a wheel stuck in a groove in the road.... routine, and implies b o r I N G. When does a groove become a rut? Too much repetition of the same changes our perceptions. We remember less, we hear less when there’s too much of the same tone, the same routines. It all blurs together, and we can lose our attentiveness. Humans are not designed to be machines. Machines are designed to do repetitive motions. Humans are designed for wonder.
"Choose your Rut Well"-- I think this cartoon means to find a situation which you can enjoy, find a way to make your current situation enjoyable, find something you are well suited for and/or something or someone to love! Because all grooves can slip into ruts if you’re not paying attention. Keep your curiosity quotient high. Wonder works wonders. 
This is one of my very early Little Savage™ cartoons from 1994. Savage and her Cat are having a grooving conversation about whether her life is in a groove or a rut.
Back then, Definition #6 was not included in Webster’s definition of “Groove”. Sometime in the 90’s, musical scholars took up the word seriously and began writing about it, dancing around the subject in academic jargon, theoretical and neurological analysis and perspectives until they had dissected the groove out of groove. They were probably “in their groove”, but like any dissection or autopsy. the living creature cannot be experienced as a corpse. Corpses don’t dance.