Why is the distribution of dark matter in a Galaxy different from the distribution of normal matter?
In the case of conventional matter, particles, atoms and molecules of it can interact electromagnetically and share energy, and they can do so in response to the effects of gravity. For example, in a (gravity-driven) accretion disc, the infalling matter particles interact strongly amongst themselves and get hot; then that heat gets radiated away and the radiating particles then cool and fall further into the gravity well. In other words, they can shed energy and then gravitationally collapse.
Dark matter does not interact electromagnetically, and thus is denied this mechanism of dissipative collapse.
This difference means that the luminous matter in a galaxy can be expected to distribute itself differently than the dark matter in that same galaxy.