A direct current (DC) of electricity is passed through the solution via anode(+) and cathode(-), affecting the transfer of metal ions present in solution onto the cathode surface, building up over time and bonding the metal onto the object.

There is a semantic difference between electroforming and electroplating; both are chemically and procedurally the same from metal to metal, but where electroplating only deposits a very thin layer of metal onto the object, electroforming is intended to build a substantial amount of metal on the object, and in some cases even supplant the object all together, leaving a robust metal shell after the object is removed.
In short:
Electroforming is when a non metal object is formed over with metal.
Electroplating is when a metal object is plated over with metal. (for example, a copper electroformed leaf that was then plated over with silver)