Black and off black are both colors; they are both shades of the color black. Black and off black both refer to the intensity of black. The intensity of a color can be decreased by adding white to it, and it can also be increased by adding black to it.
Black is most referred to as jet black. Black is associated with religion, culture, history references; in some places, black is regarded as the color for bad luck, which is used for mourning and also for evil things. Examples of black include ebony, charcoal black, etc.
On the other hand, off black refers to black, which has less intensity and looks more like a dark grey. Off black is part of a neutral color scheme. Off black has started becoming popular in the aspect of interior design, hair, and also clothing. Examples of off black include onyx, black olive, and charcoal.