Outdoor Dan had a great answer to this, just to add some clarification, the Flintlock's flash pan ignites along the side of the gun, then the spark is directed sideways into the barrel, in order to ignite the load of black powder.
An inline got the name because the primer is directly behind the black powder charge, and therefore "inline" with it. It is more similar to a modern cartridge case, without having a cartridge.
Some states my restrict what kind of black powder rifle is allowed for hunting. While many states allow inlines, there are some that want muzzle loading seasons to be more primitive and require flintlock or percussion caps.