Taberna
Tabernae were not only rooms in which merchants could set up shop, but they could also be used as living quarters. Ulpian's definition specifically states that the name "taberna" designates an inhabitable building (Dig. 50.16.183): tabernae appellatio declarat omne utile ad habitandum aedificium. We should not misunderstand Horace when he violently contrasts tabernae with the towers of kings (Carmina 1.4.13-14 pallida mors aequo pulsat pede pauperum tabernas/ regumque turris) and believe that these were residences only suited for the lowliest of people. Naturally, the wealthy would not live in these tabernae, but that is not to say that only the destitute would. Especially in the case of the Insula Arriana Polliana, a wealthy region of Pompeii, these tabernae were rather large and, as we know from the inscription, they came with a mezzanine level, a pergula.
From the Latin word pergo ("continue, proceed"), pergulae were continuations of or additions to rooms, often in the form of mezzanine floors. While one who lived in only a pergula was considered to be of lowly social standing (cf., Petronius, Sat. 74: sed hic qui in pergula natus est aedes non somniatur) nevertheless when pergulae were attached to tabernae, as they were in the case of the Insula Arriana Polliana, they made the tabernae much more attractive as living quarters. Other advertisements have been found in which the pergulae were evidently rented out separately from the tabernae (cf., CIL IV, 1136: locantur... tabernae, pergulae, cenacula... ) which suggests a significant distinction, perhaps even social, the landlord was trying to make between merely tabernae for rent and tabernae cum pergulis suis (note also the reflexive possessive adjective emphasizing the "package deal").
A cenaculum, from the Latin word cena ("dinner"), originally was a little dining room, usually in an upper story. Later it came to mean an upstairs apartment, as it does in our inscription. Though cenacula typically were inhabited by and associated with people of lower classes, this was not always the case. Suetonius tells us that even the family of the emperor Vitellius had to rent its house and move into a cenaculum when they found themselves in financial difficulty (Suet. Vit. 7). Obviously there were some cenacula that were nicer than others; In the Insula Arriana Polliana we may assume the cenacula were relatively grand as they were qualified by the adjective equestria, namely these were the types of apartments equites or knights rented. Just as the landlord wanted to contrast his tabernae to base tabernae by mentioning that they came with their own pergulae, so too with his cenacula did he want to contrast them to base cenacula by specifying that they were equestria.
Domus is the easiest of the terms to translate but perhaps the most difficult to define. Of course, anyone who has had some Latin knows it translates as "house". The question many have been trying to answer definitively is what exactly constituted a house for the Pompeians. In addition, domus is a 4th declension noun. This means that in our inscription it can be either nominative singular or plural (depending on whether the -u- is long or short). From the context of the inscription there is no sure way of determining its number so instead we must rely on the context of the Insula. Previously it was believed that domus referred to the House of Pansa itself. This, however, is quite open to objection (for arguments against its suitability for flexible renting, see Pirson 172). If we understand the term domus as simply a private house with a fauces, atrium, and a relatively spacious living area (as many houses in other parts of Pompeii were), it is more than likely that domus in our inscription is plural and refers to the living quarters on the east side of the insula which could serve as perfectly suitable rentable private domiciles to lessees of moderate, though not modest, means. Because of their size, one would not be justified in calling these eastern living quarters tabernae; that they are on the ground level precludes them from being cenacula (no matter how equestria the cenacula may have been).