The older thread is here.
I wouldn’t make a meaningful differentiation between meaning and definition. A definition is simply a description of a word’s meaning and will vary from dictionary to dictionary. (Definitions can be copyrighted.) But the meaning should be the same regardless of who writes the definition.
I think the problem is with exact, not with meaning. I don’t think that anyone would dispute that brothel and bordello were synonyms or that they had the same meaning. The quibble was over how exactly those meanings match. It is rare that two words will be used in exactly the same registers, contexts, and with the same connotations.
Look at the OED cites for brothel v. bordello:
a1593 H. Smith Wks. (1867) II. 26 Some [return] unto the taverns, and some unto the alehouses..and some unto brothels.
1608 Shakespeare King Lear xi. 87 Keepe thy foote out of brothell.
a1704 T. Brown Satire Against Woman in Wks. (1707) I. i. 84 We need not rake the Brothel and the Stews.
1711 R. Steele Spectator No. 190. ⁋2 You understand by this time that I was left in a Brothel.
1751 Johnson Rambler No. 171. ⁋12 Tricked up for sale by the mistress of a brothel.
1828 T. B. Macaulay Hallam’s Constit. Hist. in Edinb. Rev. Sept. 152 The offal of gaols and brothels.
1616 B. Jonson Every Man in his Humor (rev. ed.) i. ii, in Wks. I. 10 From the Burdello, it might come as well; The Spittle: or Pict-hatch.
1642 Milton Apol. Smectymnuus in Wks. (1738) I. 109 Proceed now to the afternoon; in Playhouses, he says, and the Bordelloes.
1719 Mr. Ratcliffe in T. D’Urfey Wit & Mirth IV. 23 Ah London th’adst better have built New Burdello’s, T’encourage She-traders and lusty Young Fellows.
1794 T. J. Mathias Pursuits of Lit.: Pt. I 19 The stews and bordellos of Grecian and Roman antiquity.
1930 E. Pound Draft of XXX Cantos xxviii. 130 And was lodged in a bordello (promptly).
1961 J. Heller Catch-22 (1962) xxiii. 236 The distant recesses of the strange and marvellous bordello.
From these it would seem that bordello carries a connotation of tolerance, perhaps even respectability. Brothel appears to be used in contexts where illegality and filth are implied. (As the brothel entry doesn’t appear to have been updated since the first edition, I wouldn’t trust this for a current definition and usage, but the comparison still illustrates how words can be synonyms yet still differ in usage.
Regarding nearly and almost, the difference is obvious. Nearly refers to “precision, closeness.” Almost refers to “degree, amount.” While they can be used interchangeably in many cases, nearly has a sense of “carefully, narrowly” and “particularly, in a special way” that almost does not. Nearly can also take modifiers, as in “more nearly,” that almost cannot.
Some examples where almost cannot be used from the OED:
1984 S. James Content Social Explan. 95 He has in mind a variety of factors, some more nearly connected than others.
1982 J. Campbell Grammatical Man ii. x. 113 These codes insure the transmission of messages as nearly perfect and free from error as the coder cares to make them.
1983 M. S. Power Hunt for Autumn Clowns 21 We would have had to wrap your sandwich in plain brown paper and that wouldn’t have been nearly as nice, would it?
You could use almost in that last one, but it would sound stilted and unnatural.