Oly - The competitive sport of Olympic weightlifting, which has 2 lifts, the snatch (bar from floor to overhead in one explosive movement)and the clean and jerk (from floor to chest height and from there to overhead).

Those who do it tend to just refer to it as weightlifting (one word), but we sometimes say Oly weightlifting when talking to others to avoid confusion with the more general weight lifting/lifting weights, which encompasses powerlifting(another competitive sport consisting of bench press, squat and deadlift), weightlifting and general resistance training.

Weightlifting is more dynamic and requires a lot of skill to control the timing and momentum, whereas powerlifting is closer to a test of raw strength(not that it doesn't require some technique).

not that any of this is common parlance:

Oly is Olympic weightlifting, a set of weightlifting movements/lifts. In various workouts, like in dieting, some folks decide on a subset of all the things (movements, food) which is good (or bad) and focuses on them. Powerlifting is another opinion of a good set of movements which focuses on weightlifting abilities.

DB is indeed dumbbell, yes

C2 is apparently Concept2, a rowing machine

Oly, the Olympic weightlifting lifts. C2 is a brand of rowing machine