Which of these is an apartment on the highest floor of a building often with terrace space?

A penthouse is an apartment or unit on the highest floor of an apartment building, condominium, or hotel. Penthouses are typically differentiated from other apartments by luxury features. The term 'penthouse' originally referred, and sometimes still does refer, to a separate smaller 'house' that was constructed on the roof of an apartment building.

While European designers and architects long recognized the potential in creating living spaces that make use of rooftops and such setbacks, in US cities, exploitation of these spaces began in earnest in the 1920s. It was a matter of news when the development of a rooftop apartment at the Plaza Hotel overlooking Central Park was announced in 1923, and this was followed by rapid development of luxury penthouse apartments in the following years.

Penthouse apartment at the top of a building on the Upper West Side, New York City.

When used as private outdoor terrace spaces, setbacks can allow for significantly larger and more protected spaces than cantilevered balconies. Due to the desirability of this outdoor space, buildings may be designed with such setbacks on more than one of its uppermost levels to allow apartments on several levels to feature such terraces. Not all penthouses have such terraces, but they are a desired feature.