Yes, it is very much like with editions of the Bible--standard divisions of the text make it possible to find a passage without having to use the same exact edition. And like with the Bible, the English version isn't the original version--and there are translations in many other languages. A French or German translation of Thucydides will use the same divisions. The usual English translations just have book and chapter divisions but some editions will further divide the chapters into sections (also pretty standard, but sometimes the Loeb edition will be a little different from the Greek-language editions published in Germany or France).
With Plato there are standard page numbers and sections of pages which go back to an early printed edition by H. Stephanus.
You mentioned the Loeb edition.
I'm asking for myself, and for a friend from a past job: do you know of any place to get the Loeb edition of various specific works (say, Abe Books or Half-Price-Books, or some universities working on digitizing their collections?) at non-exhorbitant cost?
Cheers!