Biologically, an adult is a human or other organism that has reached sexual maturity. In human context, the term adult additionally has meanings associated with social and legal concepts. In contrast to a "minor", a legal adult is a person who has attained the age of majority and is therefore regarded as independent, self-sufficient, adult behavior but still be treated as a.
In the US, for most things, you are legally an adult at age 18. In practice, I'd suggest a category called “young adults” from college age up to about 25 years old.
An adult is a person who has attained the age of majority. The age of majority is the legally defined age at which a person is considered an adult, with all the attendant rights and responsibilities of adulthood. The age of majority is defined by state laws, which vary by state.
Just about everything in all states flips to "adult" at 18 - contracts, etc. Obviously that's not 100% universal - alcohol isn't enabled until you're 21.