Question: Search intent and ranking for more specific keywords (case example)

Hey there!

I recently stumbled across a keyword that I am interested in. It has (kwfinder) a search count of 12.000 per month and a very easy difficulty.

BUT

The keyword can have several search intents - let's say we are searching for "bark", so either for the sound a dog makes or a tree's bark.
Google's first page in my example is full of results meaning "tree bark" - the meaning I am interested in. Place 1 in the SERPs is all-you-want-to-know-about-trees . com / bark (place 0 is Wikipedia).

BUT, and now my question:

Looking up "tree bark" on kwfinder shows 970 searches/month (and an even easier difficulty), but all-you-want-to-know-about-trees . com isn't even on the first page!

Why?

Why is the most relevant page for "bark" (search intent: tree bark) not even on the first page for "tree bark"?

This question is of course relevant to me:

Should I aim for "bark" or "tree bark"?

Very interested in your opinions. Thank you in advance!

(btw, #1 for "tree bark" is another-tree-page . com/tree-characteristics, so "tree" isn't even in the permalink.)