terms that are useful mainly in common language, that don't represent organisms with a common lineage

These terms are based on morphological similarities instead of molecular/genetic similarities.

• "tree" [2]
  • Trees belong to two separate phyla, the gymnosperms (which evolved first) and the angiosperms. It's not yet known whether the common ancestor of gymnosperms and angiosperms was a tree. [2] [3]
  • All trees are seed plants.
  • "trunk" is also an example of convergent evolution
• "fish" [2] [3]
  • "fish" technically includes all tetrapods [2]
  • They all fit under the subphylum Vertebrate, which includes many non-fish.
  • The last common ancestor of all fishes is currently thought to be related to the genera Haikouichthys and Myllokunmingia.
• "worm" [2] [3] [youtube]
  • They all belong under the clade Protostome, which includes many non-worms.
  • Worms are not an example of convergent evoltion, rather, bilateral symmetry is a "highly conserved" feature in the gene pool. (note that the most recent common ancestor of all bilateral animals is a highly sought-after animal in biology currently)
• "crab" [2] [3]
  • they all belong under the subphylum Crustacean, which includes many non-crabs

Terms that are useful in common language, but are almost useless in a biological context:

• "vegetable" [2]

The first group of terms are described as "not monophyletic", meaning they didn't evolve from a common evolutionary ancestor or ancestral group. They're also described as an example of convergent evolution.