If voltage is the potential, is current always within the potential?
Voltage = current / resistance.


No, voltage is the product of current and resistance:  voltage = current \$\times\$ resistance.  Ohm's law:

$$v = i \cdot R  $$


  If a circuit has no resistors, does that imply that the current is
  equivalent to the voltage(no resistance)?


If there is no resistance in the (DC) circuit , \$R = 0 \Omega\$, and thus, \$v = 0V\$

$$v = i \cdot 0 = 0V $$


  Someone tells me voltage is current divided by resistance,


Don't listen to them, they're wrong.