They say before 37 weeks, but before 36 is normally when they need a bit of extra help, after 36 weeks baby has a high chance of being fine. Preemie is a nickname I adopted along the way
Here are the defiations from Bliss, The premature baby charity
Definitions
Premature baby: Born before 37 weeks
Moderately premature baby: Born between 35 and 37 weeks
Very premature baby: Born between 29 and 34 weeks
Extremely premature baby: Born between 24 and 28 weeks
Low birthweight baby: Weighs less than 2,500g (5.5 lbs)
Very low birthweight baby: Weighs less than 1,500gms (3.0 lbs)
Even though Damien was a very premture baby, he was a high birthweight (2.635kg, or 5lb 13oz) so was as well as a moderately prem baby.