"Long grain" is just a generic classification for rice whose milled grains are at least three times as long as they are wide. (Don't worry; you don't have to be good at math to love rice.) Common varieties are usually simply labeled "long grain," but you might know them as basmati, Carolina, jasmine or Texmati.
With "medium grain" rice, the grains are less than three times as long as they are wide. Look for bomba, carnaroli, arborio, vialone, Valencia or Thai sticky rice, to name a few.
This is the last one that involves math, we promise. "Short grain" rice indicates grains that are less than twice as long as they are wide. To confuse things a bit, though, medium grain and short grain rice are often combined into this one category, which includes sushi and CalRose rice.
Short grain rice isn't a specific rice. It is a group of rice that shared similar short grained characteristics. Generally speaking, short grain rice is short and stubby. When cooked, it will be chewier and stickier than its longer grained counterparts. You can tell they are short grain by what they look like.
Use this picture as a reference for what they should look like. And many rice packages even write the words "long grain" and "short grain" on the front.