Defect Density can affect yield, but it is not a straightforward correlation.

The Defect Density is a metric related more to the quality levels of the fabrication process all else being equal. For example, the quality of the clean room (e.g. dust particles per volume), the performance of the rest of the elements of the production line like optics, motors, metal layering, etching, etc.

Defect Density is basically a baseline, which the manufacturer can use to sort of give a confidence level for their process. Specific thresholds signify different levels of confidence in the process itself.

Yield is a wholistic metric.

The most simplistic way is to define Yield is as how many dies per specific wafer on a specific fabrication run are "usable/functional." And create complex distribution models accordingly.

Those models/data are EXTREMELY confidential BTW. Since there are a lot of factors that affect them, some are straight up influenced by the fab itself, those fore mentioned Defect Densities. But a lot of it has to do with the design itself, the binning, etc. This is, things that are pretty proprietary and influenced by the designer (not just the manufacturer)

So even though 2 different vendors using the same fab may have similar baseline defect rates from the fab itself. Those 2 different vendors will experience significantly different overall yield distributions. And even for the same design, different revisions of the same design will have different yields.

Hope that makes sense.