A sarnie is a sandwich said quickly and without ceremony, and the bacon sarnie is the same bacon roll spoken in that register. The word does the defining here, not the bread. "Sarnie" is the casual, off-hand British word for a sandwich, the one used when nobody is thinking about it, and attaching it to bacon signals exactly what the thing is for: a fast, unfussed roll eaten standing up, at a counter, on a break, not plated or considered. It is the bacon butty with the formality stripped out of even the name. The bread underneath can be any of the regional rolls; the bacon is the constant; the word is the tell that this is the everyday version rather than the considered one.
As a sandwich it works because nothing about it is asked to be more than it is. Bacon is fried until the fat has rendered and the edges have caught, then put into soft bread or a soft roll that compresses around it and soaks a measured amount of the rendered fat into its base. Butter to the edges keeps the bread from going straight to paste and carries the salt of the bacon across into the bread. The sauce, brown or red, goes inside so it stays put, working as the sharp counter to a salty, fatty middle. The only craft is timing: bacon in hot, roll closed and pressed, eaten before the steam softens the bread through, so a dry top still meets a fat-heavy base. The point of the sarnie is speed, and the build is honest about that.
Said properly rather than casually, the same sandwich takes a regional word almost everywhere. It is a bap across much of England, a barm in Lancashire, a cob through the East Midlands, a batch around Liverpool and Coventry, a morning roll in Scotland, a stottie in the Northeast, a butterie in Aberdeen. The fillings branch the way the names do: a fried egg with a yolk to be managed, a sausage with or instead of the bacon, the brown-against-red question that every kitchen settles its own way. Those deserve their own articles rather than being crowded in here.