Further looking at these wallets, the only difference is that the one that is missing the 40mBTC transaction now has my password on it. The copy that has all the transactions including the 40mBTC transaction is older and does not have my password on it.
I assume that I can set the password on the correct older wallet and then delete the wallet that does not show the 40mBTC transaction. Am I right in assuming that passwords exist solely in the wallet.dat file so older, unlocked copies of the same wallet can be used to send coins without entering the password?
From the moment you copied your original wallet, they both began their own separate lives.
Encrypting one using a passphrase won't affect the other.
The only thing they share is a pool of x (with x=100 by default) pre-generated addresses.
This basically means if you click 100 times on "create new address" in each of those, you'll get the same addresses "created".
So short answer : yes. You'll be able to spend coins from the unencrypted wallet.