Is there a name for a complete word that can be obtained from another word without rearranging any letters? Sometimes the words suit each other but are not related etymologically (take the word strum in instrumental) but usually they are completely unrelated (like the ogre in progressive).

For the time being, let's call them lineagrams.

I think Anu calls them kangaroo words.

do you gnu any?

Kangaroo words contain another smaller word that is a synonym, as roo is a smaller (baby) kangaroo, e.g. illuminated contains lit.

Some kangaroo words do fall into Hydra's definition, cleanse for example, though many do not as it doesn't require the letters be adjacent.

A special case of Hydra's kind in which the whole word can be reanalyzed:
therapist = the rapist