What is the name of the current that creates the potential difference in an opamp?
It's called "input bias current", if you're referring to the current that flows into the input terminals.
See this tutorial from Analog Devices, which discusses the current in great detail. It points out that the input bias current \$I_B\$ can vary from a tiny 60 fA to many μA depending on the device. (60 fA is one electron every 3 microseconds, which is impressively low.)

You could also be referring to the input offset current \$I_{OS}\$, which is the difference between the two input bias currents.