Finned and Sashimi Fish

A finned fish is a fish (X-Wing, Swordfish, Jellyfish) in which one base line has an extra candidate, the fin, that the cover lines do not cover. If the fin is false, the ordinary fish exists. If the fin is true, it removes the digit from every cell it sees.

So only the cells that the plain fish would eliminate and that also see the fin can lose the digit. Those are usually cells in the fin's box. A Sashimi fish is a finned fish where one of the base lines is missing a corner, so only the fin and one other candidate remain in that line.

Notation

Finned X-Wing: 5 can be removed from r5c6.