Both are forms of shaming, and both are based in fear.  Fear of rejection, inadequacy, "otherness", etc. 

Examples of fat shaming:

• Judging a person's character based on their weight/shape (e.g. lazy, gluttonous, jolly)
• Making comments that a person is "overweight" and thus needs to fix themselves by losing weight (over WHAT weight? I've blogged about this in the past and probably will again in a person)
• Bashing your own body's size/shape by saying things like "My thighs are so huge." 
• Blaming a person for their health problems and blaming it on their weight

Examples of thin shaming:

• Saying "She doesn't understand me because she's thin."
• Assuming that a person is happy because s/he is thin.
• Making statements like "I wish I had an eating disorder so I could be thin." (This is simultaneously thin and fat shaming.)

Instead of judging and shaming start embracing and appreciating your body and the wonderful things it does for you.