If you "import" a private key, you are giving a copy of the private key to the new wallet to use. The old wallet still holds its copy of the private key. If two wallets hold the same private key, they both have control over the bitcoins, and both wallets will report the bitcoins as belonging to them.
If you "sweep" a private key, the new wallet sends the bitcoins to a new address that it controls (using the private key you provide). The old wallet no longer has the bitcoins.
Importing a private key can cause confusion and may create a security risk, so it is generally better for newbies to sweep a private key.
Yes, I agree with the above comment.
If someone chooses to IMPORT over SWEEP, the privatekey will be in both the old and new wallets.
It is very recommended to transfer or sweep your funds, than import the privatekey into multiple wallets.