I hope all is well. Great clarification question, so let us see what we can do to make everything clear and simplified for you.
First of all, I would like you to go to the following URL and download the PDF, as I will refer to it in answering your questions, and it is THE AUTHORITATIVE resource from NIST that sets the FIPS Standard for the use of DES and it's modes of operation.
Based on the PDF, the answers to your questions are as follows:
Is CFB Mode a block or a stream mode operation? "The CFB mode is a stream method of encryption in which the DES is used to generate pseudorandom bits which are exclusive-ORed with binary plain text to form cipher text." (Page 9)
Is OFB Mode a block or a stream mode operation? "The Output Feedback (OFB) mode is an additive stream cipher in which errors in the cipher text are not extended to cause additional errors in the decrypted plain text." (Page 12)
It allows for both if needed, based on whether there is/are partial blocks of data to be encrypted.
Now, we need to discuss what you are hearing me say in the episode, and how that is related to what I just provided to you as answers above, based on the NIST FIPS standard.
When I say that OFB operates in stream mode, we have covered that based on the NIST standard.
When I say that CFB mode operates on partial blocks what I am referring to is the ability of CFB to operate on the LAST BLOCK of data being run through the XORing process as a partial block without the need to pad it up to a full block (64 bits as an example).
I have gone back and listened to the audio for the episode as I am writing the answer to this item for you, (approx. 18:00 minutes to 22:30 minutes for this discussion) and I make this point, but I do not say specifically that the partial block being operated on is the LAST BLOCK, rather I say that you can operate on a partial block if needed without padding being required, and that you must start out with a full block size (again, using 64 bits as the example).
I can see where it may not be crystal clear as a result of my not being specific about where the partial block is in the chain, so I hope that this helps to clarify a bit.
If you are looking at the Word Doc I am using in the episode, and are using the graphic of the Cipher Feedback Mode operation, then what we are talking about is the fact that in the picture we encrypt whole blocks of the previous ciphertext, and XOR the result with the next plaintext block, to get a whole new ciphertext block, to encrypt again, etc. So we process the plaintext in chunks of whole blocks, except maybe the last partial block, where we only XOR as many bytes as we need from the last encrypted previous ciphered block.
Cryptography can be a tough subject, but it does not have to be. Remember what you hear me say often in the show, which is that the path to success for the CISSP candidate is a "MILE WIDE, BUT ONLY AN INCH DEEP"
What I mean by that is the key to success is not being focused on too much detail in any one area, but rather being focused at the right level of detail across all of the domains.
Keep asking those questions that help you t clarify issues so that you understand them, and you will be successful. :)
If I can be of any additional help to you as your journey towards the CISSP continues, feel free to call on me as needed. My direct e-mail is:
Good Luck !!