. . and very hard to answer - which is why I haven't answered it yet.
What it boils down to is individual cultivars of each general category - and good luck telling which cultivar is in the bin at your market, without 30 years experience in potato research.
Some russets, for example, are designed for French fries while others are listed as "good for fresh market, not for processing (including fries)" and they all look pretty much the same. "Fresh market" is the kind you're likely to find in your local grocery.
For frying, you want varieties with a high specific gravity. Does that help?
The most varieties (and most common varieties) listed as "good for chipping and French fries" seem to be round red and round white boiling potatoes. Probably good for hash browns too.
Of course the question is far more critical for processors and fast food chains than for home cooks who can eyeball what's going on and compensate. In any case, I'd stay away from the general purpose potatoes for frying and chipping, though Yukon Gold is listed as pretty good for French Fries.
Baking is a lot easier - russets, most kinds. For boiling, round boilers - unless the potato is supposed to thicken the soup or stew a bit, then White Rose - but not Yukon.
Anyway, I'm still researching this.