Throw out everything you think you know about this subject and start with a clean slate.
A 24 mm lens is a 24 mm lens no matter what camera body it is attached to. This is a specific specification that is attributed to the lens and has absolutely nothing to do with the camera body.
When an image from a 24mm lens is projected on a camera sensor, you can calculate what the field of view will be on that sensor.
When an image from a 24mm lens is projected on a full frame 35mm camera (Nikon FX sensor size is 35.9 x 24mm) the field of view is about 73.7°.
When an image from a 24mm lens is projected on a crop sensor camera (Nikon DX sensor size is 23.6 x 15.6mm) the horizontal field of view is about 52.4°.
As you can see, the crop sensor camera has a narrower field of view which looks like your image is magnified when compared to using a full-frame sensor.
Camera manufacturers have different lenses for their crop and full-frame sensors.
Lenses for crop bodies (DX for Nikon, EF-S for Canon) have a smaller area of illumination suitable for the smaller sensors in crop bodies. This lowers cost, size, and weight of the lens.
Lenses for full frame bodies (FX for Nikon, EF for Canon) have a wider area of illumination as compare to DX lenses. You'll find these lenses to be larger, heavier, and more expensive.
A crop body camera can accept either lenses built for crop or full frame.
Full frame bodies differ in which lens they accept.
Nikon full frame bodies can accept either DX or FX lenses, but if you use a DX lens on a full-frame body you'll get severe vignetting. Nikon can be put in a mode where the sensor will only take the center of the image effectively making your expensive camera look like a DX sensor.
Canon full frames can only accept EF lenses. If you use a EF-S lens on a Canon full-frame body, you'll damage the camera.