Dark matter is not just a mathematical construct to explain velocity curves, even though historically that was the first step. Since then, we found compelling evidence of dark matter acting as gravitational lenses. It is a very real phenomenon, as we absolutely know that there is an excess of matter that is dark, i. e. not radiating or absorbing light. Some open questions still exist about dark matter, such as whether it is made up of particles and how they are generated. But the question of whether it is real is settled.

Dark energy is more of a placeholder name at the moment to explain the accelerating expansion of the universe. It is more contested in the scientific community and there is no direct evidence of this energy yet, some cosmologists deny the existence of dark energy at all and claim that is a mathematical flaw in general relativity (the equivalent explanation of dark matter as a flaw in current models called modified Newtonian dynamics or short MOND, is a very fringe theory by now). As such, the question of whether dark energy is real is not settled, it is currently a prediction to explain some observations but lacks further evidence.