Importing private keys into wallet - does the bitcoin disappear from the original wallet? If I import a bunch of private keys into a new wallet, will the funds be removed from the original wallet? Or do they both somehow point to the same money?

In my case, I wish to move funds from Bitcoin Core wallet to an Exodus wallet.
Bitcoins are never actually in a wallet. Bitcoins sit in the blockchain. Many copies of that blockchain resides in nodes (computers). Simply put, your wallet merely is a list of addresses on which according to the blockchain are (fractions of) bitcoins stored.

You can have as many of the same wallet s you like. When they all contain the same addresses, they will show the same balance as they are all looking to the same blockchain.