Sorry. I wasn't claiming that 'route stories' was a formal name. It's just what I call them when teaching. It helps students if they can hang a concept on a name.
Most experienced navigators probably do it subconsciously. Spelling it out helps people progress in that direction by making them think about what they expect to see (and recognise when they see something they shouldn't).
As the terrain differs, so can the story. On this bearing for 500m across the flat snowfield. Then 600m on that bearing, starting to descend halfway along. There should be a little lochan to your left. From there descend the... Etc.