redundancy/lay-off

  1. More than one thousand workers now face redundancy.
  2. More than one thousand workers now face lay-off.
    Do they mean the same?
    Which sentence is more used?

They do, but I would say:
More than one thousand workers now face being laid off.

I think ‘redundancy’ is used more in the UK than in the US.

I suspect the first is most common in the UK, but ‘to be laid off’/’(a)layoff’ is also typical.

‘Lay-off’ (sometimes seen as ‘lay off’ or ‘layoff’) can also have a more temporary meaning, whereas ‘redundancy’ is more likely to indicate a permanent state from that particular job.
He faces a 3-month lay-off because of the injury.