Thanks everyone for your insights. They all help to clarify my own thoughts.
A couple of statements I have come across are quite good in defining the difference.
If you 'believe' that something is true, it is because you do not yet 'know' it to be true. Conversely, if you 'know' something to be true, you are no longer in a state of wondering whether to 'believe' it or not.

To 'believe' is to accept another's truth
To 'know' is your own creation.
Love and Light
Faune