Yes. The other replies are missing the distinction. A manufactured home is traditionally a mobile home. There is a wide range of sizes (single wide, double wide, triple wide) with a range in quality/price. These are the ones you see cut in half on a truck trailer on the highway. A more modern approach has become the Pre-fab homes. These can have a wider range of shapes than the rectangle which helps avoid the “mobile home” stigma. The manufacturing is also done in a warehouse to build pieces Of the house on a production line, like the walls, floor and roofs, that are stacked on a trailer and then erected as a puzzle on the building site. The advantage of pre-fab is that there is less waste and because components are built in a warehouse, they can be built during winter for assembly in spring. Hope this helps.

No, they can build modular homes in all sorts of different configurations. A relative had a ~2,000 sq ft house built this way, it was faster and cheaper to build than a traditional hose. It came in 5-6 sections iirc.

Doesn't a mobile home have wheel?

No. Many modern homes are manufactured off-site and then assembled on-site.