The bulk update request #2507 is pending approval.
change category short_story (1883) -> meta
change category medium_story (314) -> meta
change category long_story (735) -> meta
create implication short_story (1883) -> story (26365)
create implication medium_story (314) -> story (26365)
create implication long_story (735) -> story (26365)
create implication story_at_source (3643) -> story (26365)
change category story_in_picture (237) -> meta
create implication story_in_picture (237) -> story (26365)
create alias story_included (12) -> story (26365)
change category story_in_comments (25) -> invalid
Reason: To quote the wiki for story, "This tag may be used for related stories / backstories contained within the post itself, or outside of it in the description, or at the source."
Story in description is implying story, so I think the other tags should as well.
Short/Medium/Long_story tags indicate how "long" the story is. Or at least the wiki implies this usage. Although its most likely woefully undertagged.
Edit: added a few more tags
Updated