Hi
The tank that runs your hot water is the big tank unless you have a combi boiler or an unvented hot water cylinder, both of which come off the main. The small tank is probably the header tank for the central heating system which acts only for the heating.
If the big tank is full and you have no hot water, you probably have an airlock. If you have a mixer tap on the kitchen sink or the bath, turn on the hot (no water) leave it on and then turn on the cold at the same time as blocking off the spout, that will have the effect of forcing the high pressure cold through the hot water pipe and force any airlock right back into the big tank. Take your hand off the spout and turn off the cold tap. The hot tap should splutter and eventually clear to a constant flow. Try it.
Guy

This sounds like an air lock, a common problem. Several ways it can be sorted but the easiest is if you have a kitchen mixer tap. Place your thumb tightly over the outlet. Open the hot side first, then slowly open the cold for as long as the pressure allows. Quickly close the cold and slowly relaease the outlet. This may need to be repeated but should sort out any air lock. If you don't have a mixer tap, a piece of hose or similar tubing needs fixing between the hot and cold and the same process as before repeated.

There should be a gate valve on the supply pipe from the tank in loft to the cylinder this may still be closed. Depending on how the pipe is installed an air lock may be the cacuse

Have you opened the gate valve on the cylinder feed ?

most probably an air lock,squirt a small amount of washing up liquid into pipe from tank this will normally break surface tension in pipe and resolve problem.