What kind of siding and install type is this?
Your siding is shiplap, you can see that the grain pattern continues from the face of the board onto the lapped edge. Normally the boards are milled so that the faces fit close together, so it could be called "lap and gap" for clarity. I've no idea if that's a regional term or not.

If it had actually been made of two layers it would be board and batten, which may offer you some visually similar style products in your search. Traditionally though the batts are much smaller than the boards, and the siding is installed vertically to shed water.