Before the modern system of formal, semi-formal, and informal was consolidated in the 20th century, the terms were looser. In the 19th century, during the Victorian and Edwardian periods, the principal classifications of clothing were full dress and undress, and, less commonly the intermediate half dress. Full dress covered the most formal option: frock coat for day attire, and dress coat (white tie) for evening attire (sometimes with supplementary alternative being a full dress uniform independent of what time of the day).
When morning dress became common (in the modern sense, using a morning tailcoat rather than a frock coat), it was considered less formal than a frock coat, and even when the frock coat was increasingly phased out, morning dress never achieved full dress status.
Therefore, in the 21st century, full dress often refers to white tie only.
Today's semi-formal black tie (originally dinner clothes) was initially described as informal attire, while the "lounge suit," now standard business attire, was originally considered (as its name suggests) casual attire. Half dress, when used, was variously applied at different times, but was used to cover modern morning dress (note that the term morning dress is fairly undescriptive and has not always meant modern morning dress). Undress (not to be confused with naked) in turn was similarly loose in meaning, corresponding to anything from a dressing gown to a lounge suit or its evening equivalent of dinner clothes (now one of the more formal dress codes seen in many Western regions).