For me, yield stress (either 0.2% proof stress or upper yield stress depending on whether or not there is a yield point) is a special point in the stress-strain curve measured using a tensile standardized sample of the material in question. Therefore, it should be a stress instead of a strength. The same should be applicable to the ultimate tensile stress. It is also a special point in the stress-strain curve, namely the stress at maximum load.
However, my colleagues do not stop speaking of strength. From my point of view, the notion of strength is more related to components. Of course, I see the simiarity, which is especially obvious if we consider a tensile sample as a kind of simple component.
By the way, the pronouncation of stress is much easier for native german speaker than the pronouncation of strength ;-)