What is the difference?(in American English Language)

Without any further context the first "the yellow belt" is not idiomatic. An AmE speaker would not use that formulation without a specific reason. If you have further context please provide it.

bassaNext week you will get the yellow belt.

The people involved in this conversation know which belt they are talking about. Maybe there are a red belt, a green belt, a blue belt, a yellow belt, and a white belt on display. They look at the display and one says, "Next week you will get the yellow belt". After next week, that yellow belt will not be

By the way,

What is the difference between these to two sentences in American English Language?

Don't add "Language". Just say, "in American English".

CJ

Thanks all

No, I don't have a further context.

Don't you think that perhaps karate or some other martial arts is likely?

I'm sorry but I did not get your question.

Something like this: http://www.all-karate.com/125/history-of-karate-belt-colors

Thanks I got it.