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Strictly speaking of pop/rock music I think there is a difference between chorus and refrain. A chorus is a full blown section that has harmony, lyrics, and melody that is repeated and generally contains the "hook" of the song. The verse, like others have stated, have the same harmony and melody but the lyrics move the story along and are different from the verse to verse. It is usually not as catchy as the chorus. A refrain is mostly like a verse but instead of leading into a full blown chorus it has one line that contains the hook which is repeated lyrically and melodically.

Smoking Gun by robert Cray is the example that came to mind first:

The interesting thing about this example, and honestly one of the subtle things I love about this song is that the refrain's lyric is slightly different each time, which helps move the story along. I know this does not fit my definition above exactly but, hey, no rules in music, right?

I think the OP's idea below is correct:

I take as an example of 'refrain' the song The sound of silence, as it does not contain a typical 'chorus' but every verse ends with the song title being mentioned. That repeating line would be a 'refrain', whereas a 'chorus' would be the "We all live in a yellow submarine" part in the Beatles' song.