The wire must be marked "THWN" or "THWN-2" along its length to be used outdoors. No markings, no use. (I suppose XHHW would also be OK, but I don't think it's chemically possible to be THHN-XHHW).
It is possible to make wire dual-rated THHN/THWN. THHN is allowed 90C operating temperature and THWN is not. But obviously any dual-rated wire must be good for 90C! Therefore, a new wire type was declared, "THWN-2" which is THWN with a 90C rating. (you don't get to use the 90C rating in actual practice, but it's the basis of derates such as 310.15(B)(3)(a) which affect how many circuits can share a conduit.)
Now, for cable manufacturers, the cost difference to make a wire THHN-rated, versus dual-rated THHN/THWN-2, is rather small. So naturally, most of them make their THHN dual-rated. However, as much as you may love big-box stores, they squeeze their vendors very, very hard on price. The large volume makes it worth it for vendors to make "cheapie" price-shaved versions of their products for big-box. So it's quite possible the dual-rating was shaved off.