In photography terms, the objective is the entire sub-assembly of lens elements. Lenses are typically made up out of (at least) two central parts: The barrel (which includes the mount as well as the outer housing of the lens (including control rings etc.) and the assembly of lens elements (the objective).
With legacy prime lenses, it is most typical that the entire set of lens elements moves together when focusing, whereas more modern lenses more often employ internal focusing (IF) or rear focusing (RF) approaches, implying that focus is achieved by moving one part of the lens assembly in relation to the other lens elements. The matter is further complicated in zoom lenses which regularly function by moving a sub-assembly back & forth within the lens to facilitate zooming.
The phrase objective, is least ambiguous when referring to lenses where all lens elements form one static bloc.
Problematically – when discussing lenses in a cross-cultural contexts, most languages (other than English) use the phrase ‘objective’ to refer to what english refers to as ‘lens’: the lens (engl.) = Objektiv (german) = objectif (french) = objektiv (swedish) = objetivo (spanish) etc. Furthermore, the phrase ‘objective’ is obviously easy to confuse with the english synonym for goal (of action).
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