Roast duck vs. roasted duck

We can say ‘fried fish’, ‘baked potato’ or ‘minced pork’ using past participles for modifiers. However, ‘roast’ is different - either ‘roast duck’ or ‘roasted duck’ works, it seems to me. How should we analyze this? Is ‘roast’ a noun modifying a noun here, or is it a different form of the past participle? (According to freedictionary.com, in Middle English the past participle was ‘roste’ – does that mean that this was once a strong verb?)

Inconsistent treatment of "roast" and "roasted" goes back many years. In Mrs. Frazer, The Practice of Cookery, Pastry, Pickling, Preserving, &c (1791), the author's names for the roasts listed in a four-page "Bill of Fare" section (comprising suggested dinners of from five to seventeen dishes each) are inconsistent. Here is how Mrs. Frazer identifies the roasts mentioned in her menus:

"Roast of Beef," "Roast Mutton," "Roasted Fowls," "Roasted Hare," "Roasted Ducks," "Roasted Lamb," Roasted Veal," "Roast Beef," "Roast Loin of Mutton," "Roast Fowls," "Roasted Pig," "Roasted Goose," "Roast of Veal," "Roasted Turkey," "Roasted Turkey" [again], "Roast of Venison," and "A Roast of any kind."

That works out to three "Roast of X" (not counting the generalized final entry), four "Roast X," and nine "Roasted X." To the limited extent that any logical division in nomenclture may be discernible here, it appears that the "Roast X" and "Roast of X" formulations gravitate toward meats identified as meat (mutton, beef, loin of mutton, veal, venison), while the "Roasted X" generally applies to whole animals (fowls, hare, ducks, lamb, pig, goose, and turkey). In the case of lamb and pig, I am guessing that Mrs. Frazer has in mind roasting a very young animal whole; but that doesn't explain why she refers to "Roasted Veal" instead of "Roasted Calf," nor why she switches wording between "Roast Veal" and "Roasted Veal" and between "Roasted Fowls" and "Roast Fowls" in different instances (to say nothing of "Roast of Beef" versus "Roast Beef").

In the historical record (as reported by Google Books), authors do not appear to have distinguished consistently between "roast meats" and "roasted whole animals." I ran a number of Ngram Viewer searches for various subjects of roasting (beef, veal, mutton, pig, pork, venison, lamb, hare, goose, turkey, and duck) and found that in every instance except venison, "roast X" is significantly more popular than "roasted X," and has been so since the early to late 1800s. The Ngram graph for "roast duck" (red) versus "roasted duck" (blue) for the period from 1700 to 2000 looks like this:

I don't have a satisfactory answer to the broader question of why "roast X" has generally won out over "roasted X" in food names while (for example) "baked X" has triumphed over "bake X" and "fried X" over "fry X."

Roast is also an adjective meaning "roasted", so both words Roast and Roasted fit the definition of meat that has been cooked by roasting.