That is right.
A matte surface reflects light diffusely while glossy surfaces also produces specular reflections. More glossy, more specular and less diffuse reflection.
It is possible to have a matte and a glossy paper that, when printed with black ink, have the same level of absorption and reflectance of light, but usually the black on the glossy paper will look darker than the black on the matte paper because of the way the light reflects on the surfaces.
Let´s say that the black printed on both papers absorbs 90% of the light and reflects 10% (just to ease the math), on the matte paper we will have 10% of diffuse reflection and on the glossy paper, lets say, 8% of specular and 2% of diffuse. If you put both papers on a wall, at the eye level, the light coming from the ceiling will likely hit the paper from an angle about 30º to 45º. The diffuse reflection on the matte paper will send some of the reflected light towards your eyes, lets say half of it, so the black area on that matte paper sends 5% of the light back towards your eye. On the glossy paper the specular reflection will bounce at the same angle towards the floor, not hitting your eyes that will only see half of the diffuse reflection, 1% on this example. That makes the black on the glossy paper looks much darker than the black on the matte paper, even if both reflects the same amount of the light. You will only see specular reflection on the glossy paper if you have a light source at the opposite angle to your eyes, then you see a glare.
As our brain/eye combination compensates the white point easily, but not the black point, a interesting thing happens: the perceived contrast on matte papers varies inversely to the amount of light hitting the surface. On a dark room you have a lot of contrast, on a bright room not so much. On a glossy paper the amount of light has less influence, but the angle of incidence of the light can reduce the perceived contrast due to glare (specular reflections of lights or bright walls).
I hope that helps and forgive-me if the text is not well written, I am not used to give this explanation in English.
Best regards.