In non-technical language, as I understand it, dynamic range is is expressed in terms of Exposure Values (EV).
Although the term EV is synonymous with 'stop', it has nothing to do with DoF and refers only to the amount of exposure the sensor receives, regardless of whatever combination of F/stop and shutter speed is used to achieve such exposure.
Using the term 'stop' instead of EV is also a bit sloppy because all lenses used at the same f/stop do not let through the same amount of light at the same shutter speed. There is a varying degree of transmission loss due to the opacity of the glass and the number of elements.
If Camera A is claimed to have 2EV, or 2 stops better dynamic range than Camera B, then Camera B would need to receive two more EVs, or two stops' greater exposure than Camera A in order for the noise in the deepest shadows, at the limits of the DR, to appear the same as in Camera A, all else being equal of course, including ISO sensitivity.
However, if Camera B receives 2 stops more exposure at the same base ISO, it is likely that SNR in the midtones, including lower and upper midtones, will be better in Camera B than in Camera A, especially if Camera A is a recent Nikon, and Camera B is a Canon.
For example, you'll notice on the DXOMark site that the SNR at 18% figures (SNR around the midtones) are approximately equal for the 5D3 and the D800. If you overexpose the 5D3 shot to get the deep shadow detail as clean as in the D800 shot, then sure you'll get cleaner midtones than the D800, but you'll also get blown highlights.