Perhaps you're mistaking RSA with DSA.
DSA and ECDSA do share a lot. To construct both of these algorithms, you start with an abelian group (a set of elements (e.g. integers; one of these becomes your public key) plus a "group operation" (e.g. multiplication)) and a "trapdoor operation" which is easy to calculate in one direction, but believed to be hard to calculate in reverse. The trapdoor operation is a repeated application of the group operation.
With DSA, the abelien group is a set of integers between 1 and p-1 (p is prime), the group operation is integer multiplication modulus p, and the trapdoor operation is integer exponentiation modulus p. (Note that exponentiation is repeated multiplication.)
With ECDSA, the abelien group is the set of points on an elliptic curve over a finite field, the group operation is something called "point addition", and the trapdoor operation is something called "scalar multiplication" (which is just repeated point additions).
The rest of the DSA and ECDSA algorithm is the same, and can be defined by steps such as "repeat the group operation x times" which is performed using one of the two group operations above depending on which algorithm is being used.
RSA on the other hand is a completely different beast, and not at all similar to ECDSA.
the only difference between RSA and elliptic curve is the equation you use for the curve.
ECDSA uses a curve. Neither RSA nor DSA uses any form of curves or points.
Elliptic curve obviously uses the equation for an ellipse.
Elliptic curve crypto uses the equation for, well... an elliptic curve. An ellipse (oval), despite the similar name, is an entirely different equation.