But doesn't descent from a common root also cover the idea of a family of words like this?

cog·nate (kŏg'nāt')
adj.
Related by blood; having a common ancestor.
Related in origin, as certain words in genetically related languages descended from the same ancestral root; for example, English name and Latin nōmen from Indo-European *no-men-.
Related or analogous in nature, character, or function.
n.
One related by blood or origin with another, especially a person sharing an ancestor with another.
A word related to one in another language.
[Latin cognātus : co-, co- + gnātus, born, past participle of nāscī, to be born.]

cog·na'tion n.
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The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2000 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.