How does an electric eel produce an electric charge? I know that it can produce up to 600 volts, but what does 600 volts mean without knowing the amount of current?
The eel produces this voltage by rearranging ions in specialized muscle cells called electroplaques. While I’m not an expert in this, I suppose that they use energy derived from food to pump ions through the cell membranes of these electroplaques in order to create charge imbalances between the two surfaces of those cells. By stacking hundreds or thousands of electroplaques in series, they succeed in separating positive and negative charges to great distances on their bodies and thus produce voltage drops in excess of 600 V.
You’re correct that current is an important issue here, since even household static electricity can separate enough positive charge from negative charge to reach thousands of volts. However, static electricity can reach very high voltages because there is no current flow to deplete the separated charge. In the case of an electric eel in water, the water conducts current well enough that the eel must continue to separate charge to maintain the 600-volt potential difference between its ends. I’m not sure how much current flows through the fresh water in this situation, but I would guess that it’s at least 1 ampere and possibly more. That means that the eel is moving a considerable amount of charge each second and using in excess of 600 watts of power. If the eel were a salt-water fish, it wouldn’t be able to reach a 600-volt potential difference at all because salt water conducts current far to well and an enormous current would flow in that case.