What is the difference between
short course season and long course season?

Short course refers to a 25 yard or 25 meter pool.  Twenty-five meter meets are rather scarce, so usually the term short course refers to 25 yard meets, usually held indoors.  The winter season (October-March) is the short course season.  Long course meets are held in 50 meter ("Olympic size") pools.  These are held in the summer season (May-August) and are often outdoors, although Indiana does have several indoor 50 meter pools, for example, the IUPUI Natatorium in Indianapolis.