Bas de casse and capitale are part of the typography vocabulary.
The letters they describe are classified according to their actual shape. The haut de casse letters (i.e. uppercase) were stored in the upper part of the casse and the bas de casse (lowercase) were stored in the lower part of it.
Manuel de l'imprimerie, Casse de Gillé, 1817.
Outside a typesetting context, i.e. in real life, we call the former majuscules or capitales and the latter minuscules.
The nuance between majuscules/minuscules and capitales/bas de casse relates to text rendition versus grammar. The capitalization rules require for example that a proper noun starts with a majuscule letter followed by minuscules, e.g. France.
These rules are independent of what will actually be done when typesetting a document. For example, someone might want to write that proper noun only with capital letters FRANCE, perhaps with smaller ones after the initial letter like this: Fʀᴀɴᴄᴇ, or even only using lowercase letters france.
Whatever their choice, the F remains technically a majuscule and the other letters minuscules.