In sports it is commonplace to distinguish a "team" (as characterized by the players who took part in a match, playing together against another team), from the "score" (such as the final score of two teams having played a match against each other), and from the "ranking" (e.g. the ranking of teams within a league at the end of a season). Similarly, considering a clock it is possible to distinguish its "instants" (or "indications", as characterized for instance by the pointing of clock hands to certain elements of the clock face), along with the fact (or idea) that a clock "progresses" (considering some or all of its indications as a set in a particular order), from the "duration" of the clock between any two of its indications, along with comparisons of durations (in particular determining, durations between which pairs of indications are equal to each other), from parametrizations of the indications of a clock by real numbers (often called t).

Use and comprehension of this entire terminology then allows for instance certain parametrizations t to be qualified as monotonous wrt. the progress of a given clock (while others are not); and among those, certain parametrizations as "good" (or proportional, or affine) wrt. the duration ratios between indications of the given clock (while other monotonous parametrizations are not).

My question:

Is there a didactical disadvantage in projecting much if not all of the described clock-related terminology into one and the same word: "time" ?