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 usually well insulated and completely enclosed, with an easily closed opening on the top.
A puzzle mug is a novelty that is counter-intuitive. It will usually have several holes in the rim, making it impossible to drink from in the normal way. Frequently the solution is to cover all the holes in the rim, and then drink via another hole in the hollow handle.
