Anything before 37 weeks will be premature baby while from 37 weeks onwards you are already on full term. It depends what are the chances of birthing early because whatever we go through nearing to EDD is very much unpredictable. What you are having is mild contractions that sometimes we don't realise. In medical terms usually they will use EFM to detect baby's heart beat and your contractions.
I gave birth 36 weeks and 2 days 5 yrs ago, water broke, baby was fine and healthy but small 2.2kg only.