How much wood would a woodchuck chuck if a woodchuck could chuck wood?

A woodchuck would chuck all the wood he could if a woodchuck could chuck wood!

What is the origin of this tongue-twister and what exactly is meant by woodchuck here?

Details:

Woodchuck is used as an alternative name for groundhogs.

The etymology of woodchuck suggests that the word is not related with "wood" and "chucking" and I think the tongue twister touches on this in a humorous way because woodchucks cannot chuck wood actually. (Can they?)

From Etymonline:

woodchuck (n.) 1670s, alteration (influenced by wood (n.)) of Cree (Algonquian) otchek or Ojibwa otchig, "marten," the name subsequently transferred to the groundhog.

How did this word emerge (alteration because of similar sounding words?) and how did it end up in this tongue twister?

How is the name transferred to the groundhog?