Hi Markov...
The terminals are not at the same electric potential; there is a potential difference between them, say 12 volts for example in a typical car battery, connected or not.
You 'start a loop of current' by providing a CIRCUIT, an electrical conducting connection exterior to the terminals...those terminals are already 'connected' inside the battery via the electrolyte...an ion [charge] carrying liquid or gel...there is an electo chemical voltage [potential] ready to do work. This means ions [in the electrolyte] are immediately available to flow in the battery and provide power through an external circuit.
In the external circuit, say a copper wire and some electric device like a light or car starter, the moving charges are electrons from the conduction band of the copper atoms. Enough energy must be supplied to free electrons from their loosebinding to individual atoms...easy to do with 'conductors', difficult in 'insulators'.
for more detail, try Wikipedia under 'electrical conductor' and 'conduction band'...