Yes, drop-in and integrated are used interchangeably.
Assuming Cane Creek correctly identified the headset for your mistery frame, you should be able to use any IS42/28.6 IS52/40 pair. For the bottom part I’m pretty sure you could get away with the bearing and crown race from any tapered headset; as mentioned above, the top part may have a slightly differently sized bearing, so it would be preferrable to get the correct “IS” part.
integrated = the frame has a cup cut into the headtube.
semi-integrated = the headtube has a permanent cup fitted already that cannot be removed.
traditional press fit = you have to press in a cup
That does make sense, however most of the time “semi-integrated” refers to zero stack (ZS) headsets, which are pressed in (integrated – IS, semi-integrated – ZS, external/traditional – EC).