The numbers you are asking about deal with the livelyhood of the core in the ball. The numbers reflect the rebound factor or bounce of the ball. the .44 core would rebound less.
FYI, the core was measured back in the day by dropping it from a designated height and measuring how much it would bounce off a solid surface. I'm not sure if they still measure the core in this manner. The measurement is to insure the livelyhood of the balls are constant. I believe the .47 core is standard for school ball and is the most common for competition.
The other numbers on a softball are the compression numbers. Compression is measured by how many pounds of force is needed to compress the ball 1/4 of an inch. Compression reflects how the ball will react to being struck by a bat and how it will fly thru the air. The higher the compression number the more likelyhood of homeruns and an increase in velocity when hit. Lower the compression and the balls will seem "dead" and seem to "float" thru the air. Back in the day, many balls were identified by the color of the stitches used in the seam. I'm not sure that is a standard by all the companies that make the balls today.
Personal opinion on which softball to use; If you are playing on an all weather surface or a surface that is not natural (indoor gym flooring, concrete, rubber track) surface I recommend a lower core ball to help eliminate overbounce from striking the floor and lower compression to eliminate the height and distance the ball will travel due to lower ceilings and limited field size. If you are playing outdoors on a regulation field with normal infield conditions I see no reason to play with anything different than the recommended core and compression balls.