As I understand it, the popular assumption amongst most brewers is the definition of both is
generally: a demijohn is the 5 litre (1 gallon) container and the carboy is the 23 litre (5 gallon) container, even in the UK - think I'm correct here?
Typical Modern Demijohn:
Word Origin and History for demijohn:
n.
Probably by folk etymology from French dame-jeanne, from dame (lady) + Jeanne (Jane)
1769, partial translation and word-play from French damejeanne (late 17c.) "Lady Jane," term used for large globular wicker-wrapped bottle, perhaps because its shape suggested a stout woman in the costume of the period. A general Mediterranean word, with forms found in Spanish, Portuguese, Italian, and Arabic.
Source: Dictionary.com
Typical Modern Carboy:
Word Origin and History for carboy:
1705-15; < Persian qarÃÂba (h) < Arabic qarrÃÂbah big jug
Source: Dictionary.com
Designs of either may vary and both may be supplied with a basket.