Drift velocity: When a conductor is connected to a battery, free electrons move with a net speed which we call drift velocity. It is very small of order 10-4 ms-1 which is very small. So, we can conclude that when we switch on the bulb, it's not the actual displacement of an electron from the end of the switch to the bulb that makes it glow. Current is said to have established when all electrons start drifting in a particular direction. Current flows with the speed of light. For this reason bulb glows instantly the switch is ON despite the low value of drift velocity
Thermal velocity: When a conductor is not connected to any battery, free electrons are said to move due to their temperature & hence the name. Value of thermal velocity is very high of order 105 ms-1 but due to random motion of electrons in all possible directions their average thermal velocity turns out to be zero. Hence, thermal velocity doesn't contribute to any net current.