Maxcichon, to clarify, and I believe you got it correct; but maybe your were asking for a clarification, wattage has no relevence to the current drawn, its it is simply the resistance and applied voltage that control the current.

A 1 watt 10 watt or 100 watt rated device (resistor) would only allow the passage of a set amount of current, and the dissipation rating of the device will determine how hot it becomes or how long it will last. Woody