While there may be a part of it being "different gravity", dark matter cannot 100% be explained by modified gravity of any kind.
Why do we know this? Well there are observable galaxies that survived collisions and have been stripped of their dark matter, and the reverse is also true (galaxy-sized dark matter blobs without baryonic matter in it).
I can refer you to this wonderful PBS Spacetime video about it: https://youtu.be/5t0jaE--l0Y