Footballs and coke bottles were just that:
At one point, a "football" grip was made from an old, used college pigskin that was just too beat-up to play with anymore, so S&W would buy them up, cut out the air-bladders, and compress the leather into the shape of a grip. This was a very time- and labor-intensive process, so eventually it was phased out for the "coke bottle" grips, where old glass Coke bottles were melted down and made into grips. It was a lot faster this way, and cheaper, too. But eventually it, too, was not cheap enough, so in 1996, S&W just said "eff-it" and contracted out to Hogue, Inc. to make their 'stock' grips with the S&W logo printed in the horn, to differentiate them from the regular Hogue grips.
Target grips were made for descendants of Ed McGivern, famous revolver trick shooter, who had humongous hands. They could be made in either the Football or the Coke Bottle variants, or the cheaper wood.
Combat grips have finger grooves so that you can use the gun to pistol whip your foes without losing your grip on the gun, if you ever had to shoot it.
That just about sums it up.
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Okay, more seriously:
"Football" grips were wood target grips that had reliefs cut into the right grip panel, in the shape of a football, to allow empty cartridges to eject more easily. These were replaced by target grips that had a cut to be able to use a speedloader more easily.
"Coke Bottle" refers to the profile of the grips, when viewed from the front or back: they would resemble a coke bottle, starting out narrow-ish at the top, with a bit of a palm-swell in the middle, and then flaring out slightly at the bottom. These more closely fit the hands of many users, though they would take more time and labor to produce.
"Target" grips are larger than "Service" or "Magna" grips, and will generally fill in the area between the trigger guard and the grip frame and will fill the shooter's hand more, making precision (single-action?) shooting easier, and making the gun a little easier to hang on to.
"Combat" grips have finger-grooves (and speedloader cut-outs).
This is an example of a set of Target grips with the speedloader cut:
A set of "football" grips would not have this cut, and instead it would be a football-shaped relief in its place:
This is an example of a set of "Service" or "Magna" grips:
This is an example of a set of "Combat" grips (w/ speedloader cut):
Then you have the difference between round and square butt:
And of course, you can have round-to-square conversion grips, where the grip-frame is round-butt, but the grips are square-butt (I don't have/can't find a picture of this at the moment)
(none of these pictures are mine, and are hot-linked from other places...probably frowned upon, somewhere)
