In Germany:
Einfamilienhaus: freestanding single-familiy residence. Like House (Detached) in the OP.
Bungalow: a single-level, usually flat-roofed, Einfamilienhaus.
Doppelhaushälfte (DHH): half of a double house (Doppelhaus), the halves sharing a party wall. Like House (Semi-Detached) in the OP.
Reihenhaus: one house in a terrace - like House (Terraced) in the OP.
Reihenendhaus: like Reihenhaus, only it’s the first or last house in the terrace.
Villa: an Einfamilienhaus, but more spacious/luxurious/well-appointed.
Wohnung any apartment/flat, usually in a multi-apartment building. Mietwohnung if rented, Eigentumswohnung if owned.
Apartment: a Wohnung; a marketing term connoting a higer level of comfort.
Maisonettewohnung: a two-level Wohnung.
Studiowohnung/Studioapartment: Wohnung with a large window front.
Dachgeschoßwohnung: Wohnung under the roof.
1-Zimmer-Wohnung, 2-Zimmer-Wohnung, 3-Zimmer-Wohnung etc.: a flat/apartment with the stated number of rooms not counting kitchen, corridor, bathroom, toilet etc.: e.g. a 3-Zimmer-Wohnung could consist of living room, parents’ bedroom, childrens’ room (the three counted rooms), plus kitchen, bathroom, toilet and corridor.
Zimmer: a single room, furnished (möbliert) or unfurnished (unmöbliert), usually with use of shared bathroom/toilet.
Wohngemeinschaftszimmer: room in a (usually largish) apartment rented together with flatmates.