There are different types of houses and below is a list of typical names and their meanings:
A single-family house is not attached to any other house or structure, i.e., it is a detached house. Owner of the house owns the structure and the land beneath it. A single-family house usually has one - three stories, sometimes with a basement.
Duplex is commonly referring to two separate houses attached to each other, sharing a common wall.
Townhouses are connected to one another, usually in a row or sometimes in a square building. Each townhouse shares one or two walls with another unit, but doesn't have neighbors above or below it. Townhome owners own their units and a portion of the land on which the building sits, often including front/back yards or a patio.
Condominiums are attached to one another, just like townhomes, but a condo unit has neighbors above or below it. In a simple way to explain: if a 2-story building has 10 separate units, 5 on first floor and 5 on second floor, they are condos. If the same 2-story building has only 5 units, and each one has its own upstairs and downstairs rooms, they are townhouses. Condo units usually don't have yards, but the community may provide common areas including parks, pools, gyms, tennis courts, etc. These amenities are maintained by the Home Owner Association (HOA), which is funded by HOA fees paid by condo owners.
Structure-wise apartments are just like condos, but the difference is that apartments are rental units and the entire building is owned by one owner, whether an individual or company. Condos may be rented too, but the owner of one condo unit doesn't own the entire building.
Note that the difference between a condo and an apartment is more of a geographical thing. In California, for example, people tend to differentiate them more. But in New York, you will often hear people say they own an apartment. So depending on where you live, the definition of condo vs. apartment may be different.
A mobile home is referring to a house that is prefabricated in a factory, and then moved to a location where the house will be located, semi-permanently. Mobile homes do have all living amenities, and can be used as regular homes or temporary accommodations.
A mobile home is different from a motor home (or motorhome), which is referring to a recreation vehicle (RV) equipped with beds, bathroom, kitchen, etc., usually for camping or vacations.