The double rifle long predates the shotgun in any form. There are many examples of flintlock double rifles while the true shotgun did not appear until the percussion lock.

Prior to the percussion lock there were “fowlers”, smooth bored guns used for ducks and the like. The technique was to hide in a blind and shoot at sitting ducks. The pan flash gave warning to the birds and precluded effective wing shooting. The guns had long barrels, were heavy and unbalanced since handling was not an important consideration.

With the advent of the percussion lock wing shooting became practical and the true shotgun was developed with its balance and fast handling qualities.

As for single barrel vs double barrel, it was mostly a matter of money. The British (or Continental) hunter was likely to be well heeled and able to pay for the double. Here in America, the common man was doing the bulk of the hunting and the single barrel fit the bill. The double shotgun appeared to some extent because they are inherently cheaper in the lower grades than a regulated double rifle. Almost all the American made muzzle loading double rifles I have seen were turn barrels whch are not usually considered to be a true double rifle.

There is a miss-perception that the double rifle was developed only for big game. They were developed for all classes of shooting from rooks to elephants. The “Express Rifle” was originally developed for deer sized game, not big game. It was not suitable for big game until after the advent of smokeless by which time the term “express” had lost its original meaning and was only an ad copy writer’s term any way. Prior to, and during the advent of the “express rifle” only black powder was available and big game rifles got their horse power from VERY large bores rather than express velocities.

The turn bolt rifle first appeared as a military weapon and the spread into the sporting field. It’s true the turn bolt cannot handle the cartridge length the double can and it was not until the wide spread use of smokeless that the turn bolt could pack enough horse power into the limited case length to compete in the big game field. (Big game meaning the kind that might turn the tables, deer are "buck", not big game.)

BTW: The term “express rifle” originally meant a breech loading rifle firing a very large charge of black powder behind a light for caliber bullet to produce velocities in of 1700 fps or more. The bullets were typically fitted with wings to fit deep two or four groove rifling to prevent stripping. They were often of 0.50 caliber or so, and with the light bullet, were in the deer sized game class.