It’s a row house, nothing more, especially when your walls are attached to someone else’s walls. When I think of owning a home, it doesn’t include having someone else’s walls attached on either side of me. That’s an apartment or townhouse. Just my personal opinion. I’ve never owned a home, and have always either lived over, or under someone, or next to them.
Townhouses were the standard dwelling in towns like Bath and London. If you had the money, you would have a country estate and then a townhouse in London or whatever city you wanted to hang out in,
There were no such thing as an apartment or flat at that time. Apartments were a creation of the 2nd half of the 19th century. The townhouse was house in the sense it served as a dwelling only for a single family.
If you were in trade you would live where you worked. The baker would live above his bakery.
Poorer people would rent a room but there would be no what we would call a kitchen and like. The self contained housing unit is the apartment or flat we have today.