First off - forage caps 'are' kepis...
In clothing regulations they're referred to as 'Forage Caps' and the earlier versions with the floppy crown were also known as 'Bummer's Caps' - taken from Sherman's 'Bummers' who marched to the sea.
The Civil War issue version had a fairly long crown - giving the hat a floppy look - or if that wasn't desired, it could be sort of 'telescoped' to give it a more streamlined look - it depended on the wearer.
The later hats that were issued during the Indian Wars had a more 'structured' crown - giving the same 'look' as a telescoped crown, but without the additional fabric.
They're more 'finished' looking, if that helps...
Hats that were issued in the 1890's were definitely shorter-crowned, and you see those on Officers most often, as they could - and did - buy the latest versions.
The Civil War stockpiles were beyond vast - especially for a newly-shrunken Army that would draw from them - and the Army authorized the issue of one new cap per year, so it's understandable that you'd see both styles being worn at the same time.
Perhaps that was an idiosyncracy of the Quartermaster system of issue - with the far-flung Camps and Posts being issued last - perhaps it went by units.
That's not spelled out anywhere I can refer to.
As to what was common - certainly the soldier was issued his Forage Cap - but he was also issued a Campaign Hat during the Indian Wars, along with a Dress Helmet for more formal occasions.
On Campaign - other varieties of non-regulation headgear were worn by all ranks - and those often show in the camp photos of the time.
They were private-purchase - usually from a sutler, but also from town - and straw was popular.
Take a look at 'Parade Ground Soldiers' - by Langellier, and 'United States Army Headgear, 1855-1902' - by Howell.
Vaya,
Scouts Out!