As MaxW indicated in the comment, perovskites are a huge family of natural and synthetic compounds. Following is a breif description of the group of compounds named perovskites:
The original Perovskite is a mineral of formula $\ce{CaTiO3}$. It was first discovered in 1839 by the Prussian minaralogist Gustav Rose in the Ural Mountains, and is named after Russian mineralogist Count Lev Aleksevich von Perovski (1792–1856). The natural crystals have a hardness of 5.5-6 and a density of $\pu{4000-4300 kgm-3}$. The crystal structure of this mineral was initially thought to be cubic, but was later shown to be orthorhombic (Ref.1).
As with many minerals, Perovskite has given its name to a family of compounds with the same type of crystal structure, which are called perovskites that have a general formula close to or derived from the composition $\ce{ABX3}$. In these mineral type with formula $\ce{ABX3}$, $\ce{A}$ and $\ce{B}$ are usually two different sized cations, while $\ce{X}$ is an anion that bonds to both (e.g., $\ce{KNbO3}$). For instance, $\ce{PbTiO3}$) is a perovskite, crystals of which are Tetragonal (space group: $P_4mm$) with $a=\pu{0.3902 nm}$ and $c=\pu{0.4143 nm}$ of its unit cell. In contrast, the original Perovskite, $\ce{CaTiO3}$ crystals are Orthorhombic (space group: $Pbmn$) with $a=\pu{0.54035 nm}$, $b=\pu{0.54878 nm}$ and $c=\pu{0.76626 nm}$ of its unit cell (Ref.1).
To some extent, the multiplicities of phases that belong to the perovskites family can be rationalized by assuming that perovskites are simple ionic compounds where $\ce{A}$ is usually a large cation and $\ce{B}$ is usually a medium-sized cations, and $\ce{X}$ is an anion (if the charges of the ions are written as $q_\ce{A}$, $q_\ce{B}$, $q_\ce{X}$, then: $q_\ce{A} + q_\ce{B} = 3q_\ce{X}$). At present, many hundreds of compounds are known that adapt the perovskite structure. Few examples are $\ce{NaMgF3}$ (Orthorhombic; space group: $Pbnm$), $\ce{CsPbI3}$ (Cubic; space group: $Pm \overline{3} m$), $\ce{KCuF3}$ (Tetragonal; space group: $I4/mcm$), $\ce{LaAlO3}$ (Trigonal; space group: $R3c$), $\ce{KNbO3}$, $\ce{KNbO3}$ (Orthorhombic; space group: $Amm2$), and $\ce{(Fe,Mg)SiO3}$ (Orthorhombic; space group: $Pnma$). In fact, a perovskite structure mineral, Bridgmanite $\left(\ce{(Fe,Mg)SiO3}\right)$ is the most abundant solid phase in the Earth’s interior, making up $38\%$ of the total (Ref.1).
Figure A in following diagram illustrates an ideal cubic perovskite, $\ce{SrTiO3}$ (space group: $Pm \overline{3} m$):
The traditional view of the perovskite lattice is that it consists of smaller $\ce{B}$ cations within oxygen octahedra, and larger $\ce{A}$ cations which are nine fold coordinated by oxygen. According to this Princeton website where I abstracted the structure A (Note: I have modified to some extent):
The easiest way to visualize the structure ($\ce{ABO3}$) is in terms of the $\ce{BO6}$ octahedra (e.g., $\ce{TiO6}$), which share corners infinitely in all 3 dimensions, making for a very nice and symmetric structure. The $\ce{A}$ cations ($\ce{Sr}$) occupy every hole which is created by 8 $\ce{BO6}$ octahedra, giving the $\ce{A}$ cation a 12-fold oxygen coordination, and the $\ce{B}$-cation a 6-fold oxygen coordination. In the example shown below, ($\ce{SrTiO3}$) the $\ce{Sr}$ atoms sit in the 12 coordinate $\ce{A}$ site, while the $\ce{Ti}$ atoms occupy the 6 coordinate $\ce{B}$ site. Note that there are many $\ce{ABO3}$ compounds for which the ideal cubic structure is distorted to a lower symmetry (e.g., tetragonal, orthorhombic, etc.).
Based on these facts, your last two entries, $\ce{Pb(Zr_{0.45}Ti_{0.55})O3}$ and $\ce{Pb(Zr_{0.871}Ti_{0.129})O3}$, are of course belong to perovskite family. The first one have adapted to the structure of $\ce{PbTiO3}$ (Tetragonal; space group: $P_4mm$), which is a perovskite (Ref.1). The second one have adapted to the structure of $\ce{LiNbO3}$ (Trigonal; space group: $R3c$), which is a synthetic perovskite (Wikipedia).
There is another family of compounds with formula $\ce{A2BB'O6}$, which is called double perovskites. The crystal structures of double perovskites feature an ordered rock-salt like arrangement of corner-sharing $\ce{BO6}$ and $\ce{B'O6}$ units in the crystal structure (Figure B). This is what researchers in Max Plank Institute where I have extracted the Figure B have to say about double perovskites:
Proper choice of the metal ions $\ce{B}$ and $\ce{B'}$ and of the alkali, alkaline earth, or rare earth ions $\ce{A}$ allows to realize a large variety of physical properties in double perovskites. Prototype compounds which have found much interest are $\ce{Sr2FeMoO6}$ and $\ce{Sr2FeReO6}$ as they are half-metallic ferromagnets with Curie temperatures above room temperature and large magnetoresistance effects at ambient conditions.
The double perovskite structure is so named because the unit cell of double perovskite is twice that of usual perovskite. An example of crystal structure of a synthetic double perovskite, $\ce{Sr2FeMoO6}$, is shown in Figure C, which has a Orthorhombic (Phase Prototype: $\ce{Sr2WNiO6}$; space group: $Cmme$) unit cell (Ref.2). It has the same architecture of 12 coordinate $\ce{A}$ sites and 6 coordinate $\ce{B}$ sites, but two cations are ordered on the $\ce{B}$ site. The structure of $\ce{Sr2FeMoO6}$ shown here,the $\ce{Fe}$ and $\ce{Mo}$ atoms have ordered in a 3D chessboard type fashion.
Hence, it is safe to suggest that the compound used for first three entries, $\ce{Pb(Zr_{0.52}Ti_{0.48})O3}$, is an example of double perovskites, solely because it has a prototype structure of $\ce{Pb2FeNbO6}$ (Monoclinic; space group: $Cm$), which resembles a double perovskite ($\ce{A2BB'O6}$ type). The crystal structure of $\ce{PbFe_{0.5}Nb_{0.5}O3}$ is slightly distorted cubic ($a = b = c = \pu{4.0056 \mathring A}$; and $\alpha = \beta = \gamma = \pu{89.664 ^\circ C}$) and declaired to be a perovskite (Ref.3). On the hind site, $\ce{PbFe_{0.5}Nb_{0.5}O3}$ resembles more of $\ce{Pb(Zr_{0.52}Ti_{0.48})O3}$ than that of $\ce{Pb2FeNbO6}$.
Note: The best advice to OP is start with the book (Ref.1), which is written in basic language, understandable for any novice student learning about Perovskite materials. In addition, since OP is conveniently in England, I believe he can consult the author of the book, Prof. Richard J. D. Tilley, Ph.D., the Emeritus Professor in the School of Engineering at the University of Cardiff, Wales, United Kingdom, if OP has additional questions on Perovskite materials.
References:
- Richard J. D. Tilley, In Perovskites: Structure-Property Relationships; John Wiley & Sons Ltd.: Chichester, West Sussex, United Kingdom, 2016 (ISBN: 978-1-118-93566-8).
- Y. C. Hu, J. J. Ge, Q. Ji, B. Lv, X. S. Wu, G. F. Cheng, "Synthesis and crystal structure of double-perovskite compound $\ce{Sr2FeMoO6}$," Powder Diffraction 2010, 25(S1), S17-S21 (https://doi.org/10.1154/1.3478711).
- Renbing Sun, Wei Tan, Bijun Fang, "Perovskite phase formation and electrical properties of $\ce{Pb(Fe_{1/2}Nb_{1/2})O3}$ ferroelectric ceramicse," Physica Status Solidi A: Applications and Meterial Science 2009, 206(2), 326-331 (https://doi.org/10.1002/pssa.200824432).
