During the Renaissance, young art students were apprenticed to a master instructor who was a professional artist, and they started by copying their master's own drawings as well as drawing ancient Greek and Roman sculptures (this was called "Drawing from the Antique"). Then they studied from the live model. They only studied painting when the master felt they were ready.
This method of art training continued for hundreds of years. By the 19th century, when Europe's national art schools trained many thousands of artists a year, it was no longer practical for students to study from originals, so they copied reproductions: Plaster casts of "antique" (ancient) Greek and Roman sculptures. This is why we call these student works "cast drawings".
Students also copied lithographic prints of master drawings. The French lithographer who created the standard set of prints for French students to copy was named Charles Bargue, which is why we now call them "Bargue plates". (The original drawings, though, were by the artist and influential teacher, Jean-Léon Gérôme.)
Once students gained confidence through drawing from plates and casts, they moved on to draw from the live model. In the 19th century European academies and ateliers, the model usually took the same pose every a day for at least a week, and the student created one drawing of the pose. Art schools were national academies, and so this long-pose figure drawing was also called an "academie" (presumably shortened from a "drawing from the academy").
By comparison, in most art schools from the mid-20th century through today, students draw from the model right away, without the preparation of cast drawing, and they generally draw short poses, from 30 seconds to a couple hours, and never for more than one day. So art training for the last 70 years or so is very different from the 500 years of art training before that.
This level of drawing training was offered to students around ages of 13-18. During the 18th and 19th centuries would only study drawing during this period of their training, not painting.
To learn painting, students would then move on to train in the workshop of a professional painter. The word for workshop in French is "atelier", which is why we now call it "atelier" training.
Today, the US and Europe no longer have large, nationally accredited academies teaching classical drawing, so classical drawing and painting are both taught in private Ateliers. Juliette Aristides Atelier in Seattle, Grand Central Atelier in New York under Jacob Collins, and Florence Academy in Florence, Italy and New Jersey are some of the most well-known ateliers today. Many more small private ateliers are also listed on the Art Renewal Center's website. The ARC is the foremost and only vetting service for skill-based visual art schools. Sadie Valeri Atelier is ARC-accredited.