Here is what I personally experienced with "Web awards"
I booked a one-way web award with 50% miles discount.
As I went to the ticket office to pick up my ticket(at the time the stretch I was going to fly was not ready for an e-ticket), the lady told me she could not print out my paper ticket, because the system requires 40,000 miles instead of 20,000 web award miles. So, I phoned Flying Blue helpdesk to ask the reason why I could not have the ticket.
First, the lady did not know what to say. After a long pause, she
responded by saying that one can only have round trip web awards ticket,
hence it is not possible to print out one way ticket. So, I aked her why it was then possible for me to book that one way web award on-line, and get a booking confirmation. She said she herself could not understand why it happened, and
apologised for the whole mess.
When I reminded her that it is clearly stated on the internet, that web awards are possible either for one way or return.
Her response was this time very quick and blunt. "Sir, you cannot have a one way ticket."
Recently, I booked a reward ticket on-line.
But this time, Flying Blue charged the taxes twice on my Visa.
I don't know what will happen next time.
It must have been far better if FD had taken over FP, instead of vice versa.