Oligarchies are different from the representative democracy because in the Oligarchy only a small group of people holds power for family ties, for positions of power, royalty or military control.
In a representative democracy, people vote for a representative that defends the same ideas as them and this person will be their representative for a certain time. The difference is that anyone who can be elected a representative, there is no need for a position of power or being a part of a family to become a representative.