‘Cut nails’ are machine made nails resembling old wrought iron nails. They were certainly available back then and whoever built the house probably just had a lot of them available. They had been in use since the dawn of the Industrial Revolution, there are old mills near me that used to make them all the way back in the 18th century. They still had to compete with wrought iron nails at the time in most locations because nails were the bread and butter business of blacksmiths who were basically the hardware stores in ye olde days. Blacksmiths would have spent most of their time making nails instead of horse shoes, shovels, axes, and the like. Wire nails have to be made from steel so it took a little while for quality steel to become available at a price suitable for the market.
My house was started in the late 30s and I’ve found a few cut nails in places. I’ve found just about every kind of nail in places around this structure because any place one or two nails would do the job there are at least 5. Even the wire nails are very old and heavy. If they clinched one of those suckers (bent it over) you would not easily bend it back like modern nails made out of barely adequate steel.