Absinthe is an anise-flavored aperitif distilled from anise, Florence fennel and wormwood. Through a mistaken belief that it induced madness, it was banned almost world-wide in the early 1900's. Once it was banned, a substitute was needed, and so various companies came out with products which had a similar flavor profile, the term "Pastis" was coined by the Ricard company to refer to this product.
A difference between Absinthe and Pastis, is that Pastis will typically be pre-sweetened, while Absinthe is not.
A few years ago, it was noticed that the US ban against absinthe was specifically targeting “thujone”, which had been incorrectly thought to be hallucinogenic. It had also been incorrectly believed that absinthe should be high in thujone since wormwood, one of the key components of absinthe, contained thujone. Distillation however strips out virtually all of the thujone from absinthe, which means that real absinthe will be technically “thujone free”. This allowed producers of real absinthe to begin marketing their products in the US, as well as allowing US distillers to start producing absinthe.