I've always thought of anything that went out of the factory as intended--whether as an insert, salesman sample, or otherwise--that has a collectible error as a misprint-miscut-wrong back, etc. "Scrap" to me means something clearly handcut or uncut that did not go out through normal distribution channels. This is a misprint:
This is a scrap:
Both are collectible, IMO, so the difference is really just semantics.
Uncut sheets and partial sheets I consider a subset of scraps. They were never intended to go out that way but were likely salvaged from the trash or pulled and saved by the company. Again, doesn't really matter since they are highly sought after by collectors.