Generally, there are some differences but the differences for a given job don't usually reflect the magnitude of cost of living deltas between high-cost and low-cost areas. All three of the areas you mention are fairly high cost (although somewhat dependent on where in those areas). So, all other things being equal, people will usually be able to, most notably, buy/rent more house/apartment in a cheaper area than a more expensive one.

From the company perspective, limiting discussion to US only, the benefit of remote workers is much more about hiring talent rather than being able to save a few dollars.