People usually count reps for strength training as the rep for each exercise in a "set" is usually a smaller number 4-20 or so. With strength the exercises are challenging enough (if at the right level for you), you shouldn't be able to do more without a rest.
Usually people count cardio more in duration spent as you may be doing thousands of reps (i.e. if you are walking or running, would each step be a rep?, swimming each stroke a rep?). Often for some activities people might track distance covered--miles ran, laps swam, yards swam, miles cycled, etc. I could see counting reps in some types of interval cardio where you are doing as many of an exercise as you can in the time (i.e. how many times you jumped the rope in the minute), is that what you mean? I guess I usually count duration, but perhaps you could log the reps for the exercise in your "exercise notes" if you want a handy record. Is that what you mean?