These side-to side movements are called abduction and adduction. In order to clarify these sound-a-likes from each other, medical people will often refer to abduction as A-B-duction. A-B-duction is the action of body parts moving away from each other, or "absenting" their neutral position. Adduction is the action of body parts moving toward each other. If you are a Star Trek fan, you will know how to "live long and prosper" by A-B-ducting finger 3 from finger 4. At the same time, fingers 2 and 3 will be adducting, as will fingers 4 and 5.
What these two movements provide for pianists is the opportunity to play keys at a variety of angles. We often need to do this to play certain chord voicings or intervals that are not directly under our fingertips. These movements are made possible by the intrinsic (inner) muscles of the hands, not by the tendons of the fingers. The interosseus muscles are intrinsics located between the metcarpal bones, and they help the metacarpal bones spread apart to open the hand. They also participate in closing the hand around objects like balls and pickle jar lids. These muscles reach over the MCP joints and into the base of the first phalanges. This allows them to be part of the network for flexing and extending fingers. Performers like Pressler have very, very flexible interosseus muscles in their hands. Thanks to this muscle tone, they can play big intervals and chords despite having short fingers.
Another interesting group of intrinsic hand muscles is called the lumbricales. These are unusual muscles because they have no bony attachments. They connect to tendons. In this role, they support the flexing action of the tendons at the MCP joints. Remember the Finger Riddler, Arnold Schultz? He contended that allowing the lumbricales to work would take strain off other muscles that may be overworking in finger movement, particularly those of the forearm. Appreciating that there are indeed muscles in the hand that support the flexing movement of fingers helps us have a greater sense of the interplay between tendons, muscles and bones of the hand.
Part Five will finish this series by connecting this information to approaches to piano technique.