The type of democracy in Athens was direct (all citizens vote on all issues). The type of Democracy in the USA is representative ( A representative is elected to vote on all issues).
The citizens in Athens were people who were native and owned property. In the USA citizens are people who are over the age of 18 who were born in The USA territory or have American parents and followed the correct procedures of naturalization.
Athens laws were proposed by a council of 500. In the USA the congress present a bill.
Athens citizens had to vote. It was mandatory. In the USA the voting system is not mandatory.
In Athens there were slaves. In the USA at the beginning there were slaves but now there aren't. (legally speaking).