Quinone A, Quinone B, Ubiquinone, Plastoquinone: whats the difference?
Difference between Ubiquinone (UQ) and Plastoquinone (PQ)
Structural Difference: Structurally, UQ and PQ are very similar. They only differ in a methyl group and 2 substituents on the benzoquinone ring (Liu et al, 2016). See the image for comparison:

Functional Difference: Functionally, PQ and UQ are very different. I'll give some differentiation points:

PQ is located on thylakoids of chloroplasts (Millner et al, 1984), whereas UQ is located primarily on the inner membrane of mitochondria, though it is found in all cells and membranes (Turunen et al, 2004).

Half-life of PQ is 15 hours while that of UQ is 30 hours in spinach cells (Wanke  et al, 2000).

UQ10 influences expression of hundreds of human genes involved in different cellular pathways, and UQ10-mediated gene-gene networks are involved in inflammation, cell differentiation, and peroxisome proliferator-activated receptor signaling (Schmelzer et al, 2011).

On the other hand, the redox state of PQ pool controls the NADPH dehydrogenase complex activity and further influences on cyclic photosystem I (Ma et al, 2008).


Although UQ has more widespread effects than PQ, most of their effects are restricted to their corresponding organelles i.e. UQ mostly influences mitochondrial activity whereas PQ mostly influences chloroplast activity. This can be understood on the basis of endosymbiotic theory since mitochondria appear to be related to proteobacteria whereas chloroplasts appear to be related to cyanobacteria (Mereschkowski et al, 1905). These two are thought to be taken in by cells about 1.5 billion years ago. We can suppose that at that time, both these organisms had similar carrier molecules (since they are very crucial for metabolism). This can justify why UQ and PQ are so similar in structure. Thus, your way of distinction can be considered as correct.
Difference between Quinone A (QA) and Quinone B (QB)
Structural Difference: In many cases, both QA and QB are structurally identical. For example, both QA and QB are ubiquinone-10 in Rhodobacter sphaeroides (Laszlo et al, 2004). Thus, the main difference between the two is functional difference.
Functional Difference: The distinct physical properties of QA and QB, including redox potential, are controlled by interactions with the binding site environment. Studies have shown that the 3-methoxy oxygen of QB interacts with the reaction center backbone (specifically amide of GlyL225). This interaction pattern serves to break the symmetry of neutral UQ between QA and QB by locking the 2-methoxy dihedral angle of QB in a position conducive to electron transfer from QA to QB (Vermaas et al, 2015). In short (not going in further details), QB interacts with the amino acid residues in reaction center in such a way that QA and QB acquire large difference in redox potentials. Apart from this, since QB is more loosely attached to the membrane, it is easily detached on being reduced to QH2 for transferring high energy electrons taken from QA to cytochrome bc1-complex8.
Thus, it is hard to differentiate QA and QB on structural basis, although QB and QA have different redox potentials due to different environmental conditions. Also, it is hard to tell whether QA and QB are structurally similar in all organisms; it is only known that they both are UQ10 in Rhodobacter sphaeroides. So, there is no simple answer (yet) on whether QB converts to plastoquinone or not. But since, in Rhodobacter, QA and QB are UQ10, thus it is not possible to convert QB to plastoquinone by this species. On the other hand, in a photosynthetic bacterium Rhodopseudomonas viridis, both QA and QB are plastoquinone molecules (Deisenhofer et al, 1994). Here, there is no need of conversion of QB to plastoquinone since it is already a plastoquinone. This finding only strengthens the fact that it is not easy to give a simple answer on whether conversion of QB to plastoquinone actually takes place or not. A much similar reaction center, from a thermophilic cyanobacterium Thermosynechococcus elongatus, looks like this (Ferreira et al, 2004; Loll et al, 2005; Umena et al, 2011):

Talking about replenishment of QB, when QH2 reaches the cytochrome bc1-complex, it is oxidized back to QB. This oxidized QB can again participate in the process of transfer of high energy electrons. Thus, QB easily gets replenished in cyclic photophosphorylation.
References:

Liu M, Lu S. Plastoquinone and Ubiquinone in Plants: Biosynthesis, Physiological Function and Metabolic Engineering. Frontiers in Plant Science. 2016;7:1898. doi:10.3389/fpls.2016.01898.

P.A. Millner, J. Barber, Plastoquinone as a mobile redox carrier in the photosynthetic membrane, FEBS Letters, Volume 169, Issue 1, 1984, Pages 1-6, ISSN 0014-5793, http://dx.doi.org/10.1016/0014-5793(84)80277-X.

Mikael Turunen, Jerker Olsson, Gustav Dallner, Metabolism and function of coenzyme Q, Biochimica et Biophysica Acta (BBA) - Biomembranes, Volume 1660, Issues 1–2, 28 January 2004, Pages 171-199, ISSN 0005-2736, http://doi.org/10.1016/j.bbamem.2003.11.012

Wanke M., Swiezewska E., Dallner G. (2000). Half-life of ubiquinone and plastoquinone in spinach cells. Plant Sci. 154 183–187. 10.1016/S0168-9452(00)00200-4

Schmelzer C., Niklowitz P., Jürgen G., Okun J. G., Haas D., Menke T., et al. (2011). Ubiquinol-induced gene expression signatures are translated into altered parameters of erythropoiesis and reduced low density lipoprotein cholesterol levels in humans. IUBMB Life 63 42–48. 10.1002/iub.413

Ma W., Deng Y., Mi H. (2008). Redox of plastoquinone pool regulates the expression and activity of NADPH dehydrogenase supercomplex in Synechocystis sp. strain PCC 6803. Curr. Microbiol. 56 189–193. 10.1007/s00284-007-9056-x

Wikipedia contributors. &quot;Symbiogenesis.&quot; Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 26 Mar. 2017. Web. 14 Apr. 2017.

Laszlo Rinyu, Erik W Martin, Eiji Takahashi, Péter Maróti &amp; Colin A Wraight (2004). Modulation of the free energy of the primary quinone acceptor (QA) in reaction centers from Rhodobacter sphaeroides: contributions from the protein and protein–lipid(cardiolipin) interactions. Biochimica et Biophysica Acta (BBA) - Bioenergetics, 1655, 93 - 101.

Vermaas JV, Taguchi AT, Dikanov SA, Wraight CA, Tajkhorshid E. Redox Potential Tuning Through Differential Quinone Binding in the Photosynthetic Reaction Center of Rhodobacter sphaeroides. Biochemistry. 2015;54(12):2104-2116. doi:10.1021/acs.biochem.5b00033.

Wikipedia contributors. &quot;Photosynthetic reaction centre.&quot; Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 22 Oct. 2016. Web. 14 Apr. 2017.

Yocum, Charles Photosynthetic Reaction Centers, Univ. of Mich. 5 Sept 2008. Web. 14 Aug 2014