Our English forebears just partly anglicized a German term back in the sixteenth century.
The word that came to them was klappholt, in which holt (modern Holz) meant “wood, board,” and klapp apparently referred to the clacking sound from boards smacking together.
This klappholt and the early clapboard was used by coopers in making casks and was later used for wainscots.
The American pilgrim, however, took the term and applied it to lengths of wood that he split much thinner.
These later evolved into boards thinner at one edge, so they would underlie the board above, affording greater protection against inclement weather.