it is said that full frame aperture equivalent of 2.8 to aps-c is 4.2

Assuming same field of view, in principle f/4.2 on FF and f/2.8 on APS-C will create create identical results: DOF, noise, diffraction blur all will be the same.

In practise there may be some differences:

• FF can usually capture more light before burning, thus one may be able to use a longer exposure time to get better image quality.
• FF image is enlarged less for the final output, thus the lens can be somewhat worse to get the same resolution
• The smaller f-number requirement for APS-C may mean more complex and/or inferior optics

For most shooters it’s quite irrelevant if one uses FF or APS-C - not that much difference usually.

does it mean that shutter speed of aps-c is one stop slower that full frame on the same aperture?

Shutter speed can be what ever the user wants. If one let’s the camera to decide it instead, then an autoexposure program of the camera would likely use a different exposure time in each case, assuming the same ISO and light levels.