What's the difference between a FM & GM analysis?

I'm trying to compare the difference between a GM analysis against FM analysis. Sometimes, FM sounds more articulate than the GM and GM would not make any sense. 

Chess skill does not automatically translate to teaching ability or communication ability. Some of the best chess teachers are probably NMs. All we know from their difference in title is that the GM is an overall better player than the FM.

If GM's are better players than NM, wouldn't NM's analysis would be unreliable? I mean, most of the time, it's the NM who analyzes GM games. 

NMs understand enough about chess to explain what's going on in a GM game to a class player.   USCF NM is in the top 1% of US tournament players.  Probably only top 10% of FIDE players, but that's plenty better than the 1600 he's explaining a game to.

I feel like if the NM can explain a GM game, then why wouldn't they be playing up to the GM's level?

"I can see the combinations as well as Alekhine, but I can't get to the same positions!" - Rudolf Spielmann

So let's say you have taken lessons from a NM who explained tons of concepts to you from GM games. Are you then expected to make high-level GM moves after you digesting the information they have given you to be able to make expect level type of moves? 

I can understand most GM games, to a certain extent, after I look at them for a while.

I am far from NM level.

GM's think they are so cool

Let's say you have been explained a mathematical concept by a world-reknowned math professor. Are you expected to be able to completely understand and apply that concept immediately, and all the time in your own work?

The very best analysis is that of a GM who knows how to explain his or her ideas to the masses. 

Quite often, the next best analysis is that of a knowledgeable player (FM or even NM) who can explain the ideas, not the GM who has difficulty expressing himself. 

This is why several live chess analysis shows pair a strong GM with a less knowledgeable player who will ask pertinent questions and keep the tone light.

But let's say that the national master is watching you very closely and he's keeping track on how well you're understanding the material he's presenting to you. I personally have never had a professor keeping track of how well I'm understanding a math concept to be able to see the difference. 

As a thought experiment, what's the best way to describe the way the Knight moves to someone who has never played before?

Good teachers do keep track of their students' understanding, the problem in university is that there are usually too many students, and there tends to be an outdated/more efficient mode of pedagogy still in wide effect.

Even a great teacher will not bring a student to perfect, instantaneous understanding. It takes time for everyone. Everyone learns in slightly different ways, and at different speeds. The student's environment and particular experience have a lot to do with it.

I was teaching the Mrs. how to play chess some time ago.  She picked up how knights move right away.  I told her it's because women's brains are illogical so the knight move made sense to her. 

Closest square not on the same rank, file, or diagonal is how I do it.

I would think they would vary between player to player as opposed to title to title. At best guess a GM have may a bit more experience with a very particular posistion in a very particular game so he might have more personal thoughts. It's hard to image any fundamental margin between the the 2 title classes since you'd expect both to be fundamental to say the least. 

Really? Seems like that would take much longer than just saying. "It moves in an 'L' shape".

Unless, I guess, your student is Chinese and has no idea what an 'L' is.

I think the explanation in Bobby Fischer Teaches Chess is probably the worst I've seen. 

My favorite is: The Knight jumps three squares and falls over one. Or, on a bad day, jumps one square and falls over three.

The most mathematical went something like: the Knight moves one square vertically or horizontally, like a rook, then one square away from its point of origin diagonally, like a bishop. It cannot land on a square occupied by a piece of the same color. It is the only piece that can jump over other pieces.

Lasker's description is a full paragraph. I'm not sure I would understand what he was talking about without diagrams.