A striking personal example of your account pictured in the question was my experience where I had to type in my PIN at the bank counter on a keypad. It turned out I entered it incorrectly several times in a row, despite the fact that I had used that PIN a zillion times on ATM machines. Luckily, the bank employee had seen this phenomenon many times before, and she explained to me that the standard computer keypads have a different numerical layout than ATM machines. So to type in my PIN correctly I had to do it under visual guidance - an awkward experience. It showed quite strikingly that I had been entering my bank PIN using motor memory.
Much of our motor behavior is learned - think of learning to walk, cycle or ice skate. To achieve motor learning, the central nervous system is believed to use internal models that predict the mechanical dynamics necessary to execute a task. In theory, the internal model is an association from a desired trajectory for the hand to a pattern of muscle movements. This map is basically unique for the objects that we have learned to interact with. Because we routinely use our hands to interact with a remarkably diverse variety of mechanical systems, the ability to learn and recall internal memories is thought to be a fundamental property of the motor system (Shadmehr & Brashers-Krug, 1997).
Shadmehr & Brashers-Krug, J Neurosci (1997); 17(1): 409-19