Slitherine

I apologize for the somewhat obscure and abbreviated title, but I think you can figure it out.
I am quite new to FoG, though I have a number of the army books. One thing I was wondering, as I was going over the rulebook, is to what extent the Renaissance and Napoleonic 'core rules' differ. Obviously the latter two will have a number of new troop types, but are the rules for cavalry charges, etc. identical?
More to the point, when the rules do differ, are these rules 'added on', so to speak, or are they alternate means of situation resolution?
One reason I am asking is because the Renaissance book looks a bit cleaner in organization and, if it's not too much difference, I'd rather read it than the A&M book I have. But if there's significant departure in rules I will start with A&M, since that is the era I intend to play in.

The two rule sets share the same 'ethos', element based battle groups which move in very similar ways, charge in similar ways, shoot in similar ways and melee in similar ways. But there are some significant differences:

FoGAM has impetuous troops that can charge when you do not want then to FoGR does not.
Shooting capability is included in the impact in AM and not in R.
Shooting in R is a lot more effective especially gunpowder weapons.
Infantry (especially pike and shot) are less manouverable in R but cavalry more so.
Infantry cannot be deployed in the flank 12" sections of the board in R in AM they can.

I am sure I have missed some but I think you get a flavour of the differences. Which to choose first? I would choose AM as I think it is a 'fuller' game.

Hope you have fun either way.

FOG N is an entirely different game.
Mechanisms different. Sequence of play difference. I joke that after the word "glory" in the title it is entirely different. Truth is you can see the similarity, but it is 95% different mechanisms. They mistakenly use similar terms. So if you play both you can confuse yourself, but they are very different. An example in FOG N shooting causes hits which create an outcome. Flat out. In A&M shooting causes hits, then you roll for what the effect of those hits are.

FOG R is more similar to A & M and is a natural progression.
Mechanisms are virtually identical. Period differences for troop types and interactions adjusted.
Because of the deadlier impact of gunpowder the game is "bloodier" in the sense of taking off bases and has more attrition aspects that many seem to enjoy.

All 3 have the construct your own army to points model. I have played a number of FOG N non-points historical and found it very, very good for that.

Two more things about FoG:AM to FoGR, there are a couple of identical terms that mean different things between the two sets which can be confusing if you switch frequently, and because most of the foot shoot the game plays very differently. In my opinion the FoG mechanisms work better in FoGR.

For a general introduction, you could read either book. But if you intend to play A+M I'd read that because otherwise bits from FOGR will lodge in your head and confuse you. For example, there's quite a bit of difference in the fomation rules between the two (A+M is straightforward, R is more complex to reflaect Tercios. pike and shot, etc.)

What I'd suggest is read A+M. Skim read it a bit until you get to the first movement rules (until then the rules are a bit wordy I think with the intention of introducing a non-wargamer gently). Be prepared in your first few games to be leafing backwards and forwards to find the relevant rule (we all did that). Though the v2 index is a good one (v1 was not).