Well, they mean pretty much the same thing. To make fun of somebody requires at least a small amount of creativity. To simply laugh at someone is just to laugh mockingly at them in response to something silly or stupid they've done. But they both involve mockery and disrespect. Note the difference between "laugh at somebody" (mock) and "laugh with somebody" (join with them in laughing at something else). Btw, you mean "laugh" not "laught". And (at least in my opinion), it gives a wonderful impression of respect and love for a language if you correctly spell out words (in questions about language), rather than abbreviating them. If I were the word "somebody", I would feel very un-loved if somebody spelled me as "sb.", especially in a question about language. Poor word. Are you in such a hurry--or do you feel that an answer is so unlikely--that it's not worth the time and effort to write all of the letters in a word? :D

When you laugh at somebody, it is a passive response. You yourself are not making any (cruel) jokes. Laughing at somebody may hurt their feelings or it may not, but it is just a reaction and it's not meant to be unkind. For example, perhaps you've seen the video of the person being interviewed on live TV in his home office, interrupted first by his four-year-old daughter who comes prancing in, and then a baby in a walker. Everybody laughs at the children because they're so cute and behaving in the way children behave. That's "laughing at" the children, not "making fun" of them. https://www.youtube.com/watch?v=QU48FaWx7cM Making fun of someone means making jokes, often mocking, or doing crude imitations, of somebody. For example, US President Gerald Ford had a couple of clumsy moments when he stumbled and fell. Comedian Chevy Chase on "Saturday Night Live" had a series of sketch in which he imitated Ford and was constantly falling down in funny ways. Chase was making fun of Ford, and Ford's occasional moments of physical clumsiness. https://www.youtube.com/watch?v=tF98NkctXDU

The man fell over and split his trousers. The onlookers laughed at him. The man was embarrassed. Some of the onlookers were kind and they quickly stopped laughing at him. But others were not so kind and they made fun of him. They called him names and made rude jokes.

Make fun of somebody-- You are saying mean things about them to be funny. "Teasing" is another word for it. Sometimes it's truly mean, and sometimes it's just friends joking. examples: We were making fun of John because he wore a weird hat. We were making fun of John's hairstyle. We made fun of the way John talks. Laugh at somebody-- It can mean the same thing, but it can also mean someone did something embarrassing and you are laughing about it. Or, someone else made fun of them, and you are laughing about it. examples: We laughed at John when he tripped. We were laughing at John because Sarah made fun of his hat.