If you wire a separate circuit does that do the same job as a GFCI?
GFCI (ground fault circuit interrupter) has nothing to do with what the circuit is on. 

Essentially, a GFCI shuts off if the current on the hot and neutral wires are not equal. This happens when there's a literal ground fault (hot has some pathway to ground, such as through frayed insulation), or there's a dangerous situation, like current is flowing through a person or through water and going to another ground (like a water pipe). 



A GFCI can operate independently on a circuit with other non-GFCI outlets, on a dedicated circuit, and it can also protect other downstream outlets. There are also circuit breakers with GFCIs integrated that protect the entire circuit.