Do grandmasters ever disagree on what the main purpose of a move was? I don't mean disagreeing on which move should be played, but why the chosen move was played.  The reason why I ask is because if I study a game and read the annotater's explanation, I tend to ask myself if other grandmasters annotating the game would say the same thing or not, or perhaps agree partly but add more important explanations that were not mentioned.  Has anyone encountered this before?  The only reason why I haven't is because I've always only had one annotater to read from regarding a specific move when studying a game (I mean verbal commentary), so I don't get a chance to compare.  

For example, one grandmaster says "Played to protect the weak square on e5", and then another says "The piece moves out of the way so that a2-a4 can be played and launch a minority attack.", so they are really saying different things on what the primary purpose on the move was.  Perhaps the first annotater said what he said because the minority attack (or a2-a4 even) was never actually played due to change in circumstances, while the second annotater saw that the minority attack was the original plan but it was changed shortly.  Or perhaps the second annotator was wrong about the move's primary intention (perhaps the minority attack was just a secondary possibility) and it really was meant to protect the e5-square, and that is why a2-a4 was never played.  I just made up that hypothetical example of course.  You can imagine similar "arguments" between grandmasters.
The short answer is "Yes, they most certainly do". Not only that but they often disagree on whether the move is a good move or a bad move! This kind of thing comes from players and annotators having preconceived ideas about the players whose games they are annotating rather than because they are trying to deceive possible future opponents or keep important analysis secret. Players who still have such secrets to keep rarely if ever annotate games and if they do will be mostly bland and just follow the kind of analysis you would get from a computer.

Here is a concrete example of some very explicit disagreement from John Nunn's latest book "John Nunn's Chess Course". It's worth quickly saying that it's not really a chess course. Rather it is an excuse for John Nunn to publish very detailed analyses of some of Lasker's games disguised as a chess course ;-).


  The second example is from much later in Lasker's career ...
  
  It shows how once a narrative is accepted, the analysis is then
  shoehorned into being consistent with it and objectivity is thrown out
  of the window. The numerous spurious improvements for Black bear
  witness to the power of the consensus and only serve to obscure the
  real point that Lasker skillfully led the game into a deceptive
  position that appeared much better for Black but was not.
  
  This time the references are to Why Lasker Matters by Soltis
  (Batsford, 2005) and Emanuel Lasker Games 1904 - 1940 by Soloviov
  (Chess Stars, 1998). ... This is another game which has been
  considered little more than a swindle, and it's interesting to see how
  Soltis and Soloviov jump through all sorts of analytical hoops in
  order to keep the narrative intact.


There then follows a detailed analysis of the game interspersed with criticism for Soltis and Soloviov for just getting the analysis wrong. Nunn clearly has a very high opinion of the longest reigning world champion and believes that critics have often done Lasker an injustice which he puts right.

Note that the analysis that Nunn takes issue with is relatively modern. It is not that computers weren't available in 1998 and 2005 for Soloviov and Soltis to use to check their analyses rather that they neglected to use them because they had already made up their minds!