It's a single family home. That says nothing about what type of building it is. It only means that it's a home with one kitchen, one main entry, that is one dwelling unit unattached to any other dwelling units, unlike an apartment building or duplex that contains two or more separate living units under the same roof or sharing walls. I'd say you have a mobile/manufactured home with additions.

single family modular.

Originally a trailer was placed on the lot, but overtime a previous owner poured a foundation, basement, built on a living room, dining room, and 2 bedrooms. It's sided and from the outside it looks like a single family home. Only a portion of the trailer is left (kitchen, bathroom, and small bedroom). A portion of the frame to the trailer is mounted onto the foundation. New plumbing and electrical have been inserted. By portion 2/3 of the home is framed and drywalled like a house. Is this considered a single family home? Or is it manufactured? Or something totally different?