The first one is just a washing, followed by filtration because there is only one liquid phase and notably, the ethanolic aqueous thiosullfate solution.
Purification occurs because TBABr3 reacts with Na2S2O3, forming minerals, which are water soluble.
Bu4N(+),[Br2.Br(-)] + 2Na2S2O3 → Bu4N(+),Br(-) + Na2S4O6 + 2NaBr
On the other hand, the unreacted alkene (if any) and the formed TEAB are soluble in ethanol.
Obviously, this technique can be applied only when solid and/or ethanol-insoluble dibromalkane derivatives are formed, e.g. bromination of stilbene.
In contrast, the other two procedures are extractions because they are two liquid phases, in which the product and the impurities are selectively dissolved, respectively and it can be applied when liquid bromalkanes are formed.
In addition, the other two procedures are "reactive" extractions because the main impurity (excess of TBABr3) reacts with the aqueous solute (Na2S2O3).
Berthelot and Fournier: J. Chem. Education, (1986), 63, 1011, can also be found in the link, below:http://digicoll.library.wisc.edu/cgi-bin/JCE/JCE-idx?type=article&did=JCE.JCE06311.i0058&id=JCE.JCE06311&isize=XL