In photography magnification is a ratio. The ratio itself is:
Size of the subject reflected on the sensor/film by the lens : Size of the subject in real life
So a magnification of 1:1 means that the image is reflected on the sensor at the same size as it is in real life. As a result when two lenses of different focal lengths are set so that they are focusing a subject on the sensor at the same magnification, the frame covered by both lenses will be the same; because the subject itself is being reflected at the same size onto the sensor by the lenses.
What will change is that the shorter focal length lens will render background details more clearly, whilst a longer focal length lens will render a quicker fall off into blurring; oft you have to compare extremes of focal length to see this effect clearly - a 90mm and 105mm would be almost indistinguishable, whilst a 150mm to a 35mm would show a more marked difference.
Note that also when dealing with magnifications the depth of field at the same aperture* will also be the same no matter the focal length.
*note most modern macro lenses internally change their properties. The focal length as you focus closer to 1:1 often reduces, similarly the effective aperture gets smaller (you can see this as most macro lenses get a little darker through the viewfinder). As a result you might have the lens set to f2.8, but the actual aperture might be closer to f5.6. Note that Nikon camera bodies do show this change in effective aperture to the user, whilst Canon ones do not. So a Canon shooter can take a shot at f2.8, whilst a Nikon photographer with the same lens (eg a sigma lens) cannot.
The actual aperture in both cases is the same, the camera bodies are just reporting things to the user differently.