What is difference between Advance Teleport and Random Teleport?

A random teleport is used from your items and will move you to a random location in your current state. The advanced teleport is needed to move to a chosen spot. To use these go to the map and select a location in your current state and chose the teleport option.

You can also use advanced teleports to travel to other states during cross state events (clash of zones kill events / doomsday conquest. Although you have to move back again. (It is not a permanent state migration.)