There are two main ways to build a house out of wood. You can go for stick-built construction or timber framing. Homes in the US were mostly timber framed until the early 1900s. Advancements in tools and manufacturing techniques has resulted in stick-built homes becoming dominant in the US since then.

If you search for “stick-built” you’ll see pictures and encyclopedia articles describing it. The basic idea is that you take standard dimensional lumber (like 2x4s), bring it onto the site, and assemble it into the frame for the house. Timber construction uses larger pieces of timber to make the house.

I’m not an expert but it seems to me that stick-built construction took over the country because of advancements in fasteners. If you tried to make a stick-built house in the 1800s it would fall apart, but this is the 2000s, and they make a million of them every year.

The availability of engineered wood products like plywood is a big part of it too. Being able to attach what's effectively a solid sheet of wood to a wall adds a ton of shearing strength, for example. (And that's without getting into fancy modern engineered wood products like parallel-strand lumber or glulam, which give you something even better than raw wood.)