How do long-, medium-, and short-grain rice differ?

Long grain is simply a generic classification for rice that has milled grains  at least three times as long as they are wide. Common varieties are usually labeled long grain, and include basmati, Carolina, jasmine or Texmati.
 
Medium grain refers to rice with milled grains less than three times as long as they are wide. These include bomba, carnaroli, arborio, vialone, Valencia, and sticky rice, to name a few.
 
Short grain indicates grains that are less than twice as long as they are wide. Medium-grain and short-grain rice are often combined into this one category, which includes sushi and CalRose rice.
 
Source(s):
Whole Foods "Guide to Rice"