The first word, dual, can be either an adjective or a noun. As an adjective, dual means that there are two of something, and usually two parts of the same thing.Dual can also mean two things that belong to the same thing or person.
Examples:
1. James put new dual speakers in his car that sound really good!
2. The word "like" has dual meanings in English.

Duel can be both a noun and a verb, but as either one it refers to a kind of fight. As a noun, a duel is a fight or competition, usually that two people agree to have, for the purpose of settling an argument.When duel is a verb, it means "to fight" or to participate in a duel with someone else in order to settle an argument.
Examples:
1.The knight challenges the man who insulted him to a duel, so that he may defend his honor.
2. Susan sees two children dueling with pretend swords in the park on her way home.