Do "oak" and "door" come from the same ancient word?

I saw that assertion in The Overstory, but couldn't find the connection with my usual dictionaries, so I turned to artificial intelligence.  Twice.  Here's the first reply:

Yes, "oak" and "door" share a common, ancient linguistic origin, specifically rooted in the Proto-Indo-European (PIE) root *𝑑𝑜𝑟𝑢−**𝑜𝑟deru- (meaning "tree," "firm," or "solid") and the Celtic/Gaelic word duir (meaning oak).

$*doru-**or**$

This connection stems from the historic use of durable oak wood for creating sturdy doors.  

Key details regarding this etymological connection: 

• The Connection: The Celtic word for Oak, "duir" or "dair," is believed to be the root for the word "door," reflecting the oak's strength and its role as a solid, protective barrier.
• Tree of Knowledge: In Celtic tradition, the oak was seen as a "doorway" to the spiritual realm, further strengthening the linguistic link between the tree and the concept of an opening or entrance.
• Related Words: The same PIE root (*deru-) is believed to be the ancestor of several related words, including "tree," "true," "trust," and "Druid".
• Alternative View: Some linguists note that "door" (Old English duru) descends from a different PIE root (dʰwer-) and that the connection to "duir" may be partially driven by cultural or folkloric ties rather than strict linguistic derivation.

*Note: While many sources highlight the "duir" (oak) to "door" connection, the exact, direct phonetic evolution from that specific Celtic word is debated by some linguists who prioritize the dʰwer- root, though the cultural association remains strong.

Blogworthy for English major readers, I thought.  But when I double-checked before posting this to the blog, I received a rather different reply:  

The short answer is no, the English words "oak" and "door" do not share the same etymology. While there is a common folkloric connection between them, linguistically they stem from distinct Proto-Indo-European roots. 

Linguistic Origins

The confusion often arises because the Celtic word for oak sounds similar to the English word for door, but they are historically separate:

• Oak: Derived from the Old English āc, which comes from the Proto-Germanic *aiks.
• Door: Derived from the Old English duru, stemming from the Proto-Indo-European (PIE) root *dʰwer-, meaning "doorway" or "gate". 

The Celtic Connection

The perceived link is primarily found in Celtic languages and mythology rather than English etymology: 

• Daur/Duir: The Old Irish and Gaelic word for oak is daur or dair.
• Symbolic Meaning: In Celtic lore, the oak was considered a "doorway" to other worlds. Because the word for oak (duir) and the word for door (doras in Irish) share a phonetic resemblance, they are often linked in spiritual or "folk etymology" contexts.
• Druids: The term "Druid" is widely believed to be a combination of the root for oak (deru-) and the root for "to know" (**weid-), meaning "oak-knower". 

Root Comparison

Word	English Source	Ancestral Root	Meaning
Oak	āc (Old English)	*aiks (Proto-Germanic)	Oak tree
Door	duru (Old English)	*dʰwer- (Proto-Indo-European)	Doorway, gate

While the Irish word for oak (dair) is actually a cognate of the English word "tree" (both from the PIE root *dóru), it is not a cognate of the English word "door".

I think I used the same AI each time (Google), but I may have phrased the question slightly differently.  The information is basically the same in both replies, but the connotations are dissimilar.  Perhaps the first time I just inserted the phrase and the second time used the word "etymology."

Interesting and instructive re the proper use of this new technology.  I'll also note there are formatting glitches up above because I can't write or edit in code, so oddities sometimes spill over that I can't correct.