Here's the deal - you should rarely attempt to use either until you've developed a strong relationship with the reporter. You should approach every engagement with a member of the media as if you were not only "on record" but that every comment, pause, and break in conversation is going to be transcribed and printed/published/broadcast.
From the moment a reporter contacts you, it is "on record." Maybe you aren't prepared to speak on the subject and need to coordinate a response. This is totally fine, and 99% of reporters know the score. But rather than stating "I don't know," tell the reporter that you don't have that information at the moment and ask what their ultimate deadline is. Then you get to work.
Prepare your response and deliver it to the reporter. Nine times out of 10, they will have a follow-up question that you may or may not be prepared to address. Sometimes you will need to be firm and refer back to the statement, and other times, there may be a need to provide additional information "on background." Before doing this, you must obtain the reporter's agreement that you are going "on background," and even then, be cautious with the information you are sharing if it is related to a crisis or sensitive issue.
With regards to "off the record," I highly suggest that you stay away from that unless you have a high degree of mutual trust with the reporter.
I've had five reporters that I trusted enough to go "off the record" over my career. One is retired, one is in another field entirely, and the other three are still getting bylines. But those relationships were built over the years and not overnight.
That being said, if you do go down this path, ensure that you discuss with the reporter what your definition means and obtain an agreement. If you can't come up with a shared definition or the reporter doesn't agree to maintain anonymity, walk away.
So when in doubt, never use "off the record" with reporters.