A safety sausage to my mind is an open ended fairly small noticable bag designed to be inflated on the surface to wave at the surface support.
A DSMB is (these days) normally self sealing meaning it wont deflate if its not held totally upright. They also have overpressure dump valves to avoid them exploading and tend to be taller than sausages.
My DSMB is pretty standard and its roughly 1.5m tall.
As for BSAC requiring it for non deco dives - dont forget BSAC is a british orientated dive organisation. DSMBs are pretty much mandatory and i doubt you'd get on a boat without one for any dive (certainly most clubs wont even let novices in the water without one).
In typical british waters you have low vis and strong currents and its VERY unusual for any dive to result with an ascent up an anchor line.
You jump in, do the dive, shoot the bag and the surface support can follow the divers that way even in strong seas/current.
Regardless of deco/non deco dives its a sensible idea in those conditions so i can see why they enforce it.
Personally id like to see the DSMB training made mandatory in the lowest (ocean diver) grade. As it is, its not required but all clubs i know of teach it anyway.
As for how to inflate, several methods, all personal preference. The buddy ones have a self inflating bottle. Other people use exhaust gas to blow into it (from depth typically 3 breaths is enough) and others (like me) use my octopus.
There are pros and cons to each method.
The reel is never ever clipped to yourself and even a lanyard is not recommended on the reel. If a boat prop tangles in that wire you're going up quickly, if its not attached to you its just the bag and reel you lose, not a limb or worse.
Its especially noteworthy in areas with jetskis who seem to see the bright orange bag and regard them as guides for a slalom run.