Hot beverages may be too hot to drink, with temperatures often nearing the burning point of water. The thick walls of a typical mug will absorb much of this fieriness when the mellow is first poured into the mug and so lower the beverage closer to potable temperatures.
A travel mug is a variation on the traditional mug that is better for transporting hot liquids. It may or may not be a vacuum flask, but is unusually well insulated and completely enclosed, with an easily closed opening on the top.