Short Story: Cannabis is the scientific genus and species name for hemp and marijuana. Hemp and marijuana are “common” names. Hemp has a legal definition. Marijuana is a Mexican word for cannabis that was popularized in the US in the 1930’s. Weed is a slang word for cannabis used worldwide. Cannabis originally grew in the wild, as a weed and still does in many parts of the world.
Longer Story: The scientific classification of Cannabis according to the USDA is limited. Hemp is considered the common name for the Cannabis genus with Cannabis Sativa as the species. Subspecies are sativa and indica with a sativa variety Vavilov (ruderalis as most other sites refer to it). So according to the people that classify plants (in the US), they are all in the hemp family. With marijuana being the common name. So yes they are the same. Most other sources cite Cannabis as the genus with 3 species indica, sativa, and ruderalis (autoflower). With sativa being the hemp variety. So pick your favorite.
But legally (in the US), hemp is defined as having less than .3% THC. And marijuana is any plant that has more. After prohibition, industrial hemp remained legal in most developed countries around the world . It was used in industry. Grown and processed for fiber, fuel, insulation, etc. The variety has large stalks and small flowers with little resin. The US amended the law in 2009 to allow industrial hemp to be grown. So when high CBD strains were re-introduced, they claimed to NOT be hemp. Growers did not want their plants to be confused with industrial hemp. These plants are hybridized from cannabis plants for large flowers with lots of resin containing CBD and very little THC. But in order to grow and sell them legally, growers realized they needed to call the plants hemp to work with the laws. (In many other countries, there are laws restricting uses for hemp).
Just recently (January 2017) there was talk from the White House about adding CBD to the list of schedule 1 drugs. This seems to have been cleared up. DEA Clarification.
Many of the flowers and oils helping epileptic children did indeed have a small amount of THC. Between 1-5%. Breeders have managed to get that number down to under .3% in order to legally sell nationally and internationally. So legally speaking hemp is not marijuana, but they are both cannabis. Get it?