The difference between a miscarriage, stillbirth and premature birth is the length of the pregnancy and condition of the baby. Prior to 20 weeks whether the baby is dead or alive it is a miscarriage (also called spontaneous abortion). After 20 weeks if the baby has died it is a stillbirth. Once the baby is viable (currently after the 24th week) until 34 weeks a live baby would be considered premature (this varies some doctors say until 38 weeks).
So the delivery of a 34 week live baby would be considered a premature birth. There is no way it could medically be considered a miscarriage at least not in today's terminology.
If your mom did not have real contractions then she may have had an incompetent cervix which causes painless (or sometimes with mild cramping) dilation.
Some women have contractions but don't realize it since they're not painful (my MIL woke up with one of her 11 babies pushing; never had much for contractions).
Some blessed women have interrupted nerve flow to the uterus and do not feel the contractions at all.
If a woman does not have an incompetent cervix she will have contractions; whether she has one or one thousand of them it is necessary to open the cervix and expel the baby.
I do not know if there is any scientific evidence proving whether or not extreme emotional/mental distress can cause miscarriage/stillbirth or preterm labor.
I can understand why this is important for you to know. I hope I've been able to explain things clearly enough. I'm not sure what you had hoped to hear but regardless of how you came into the world it's a blessing to know you did
Love and Prayers, Kelly
P.S. I am a twin. We were born 8 weeks premature. I was told for 25 years that my brother was older than me (so that I would always have an older brother to look out for me). While at a restaurant one night with my mom and a friend I told my mom rather flippantly that I've always had a hard time believing my brother was the older twin because I've always felt like *I* was the older one. She looked me straight in the eye and said: "you are". It doesn't make a difference in the world who is older but knowing made a difference to me. I'm glad that I know.