I think a normal birth is one where a mother is empowered and able to make decisions about what she would/wouldn't like to occur during her birth with the full knowledge of what each decision might bring about. A normal birth is one where the mother and baby's physical and emotional wellbeing take precedence. Only very, very few births if approached in a normal way would end up with an emergency outcome.

An abnormal birth is one where she is coerced, has information withheld from her (during pg and birth), is bullied, pressured to experience something that makes her uncomfortable, scared, or whatever situation she may find herself in that does not allow her to come to an informed and empowered choice. I also take this to mean information is not generally available in her culture (be it developed or developing!), so it may be superstition or medical in nature.

I do not think a normal birth needs to exclude medical assistance, just like helping someone who is sick doesn't mean the automatic inclusion or exclusion of medication, as well as natural remedies and helping your own body. But I think it's highly unlikely that most birth interventions are offered with the full knowledge of the mother as to all possible implications of those interventions. I don't think our culture is always conducive to having a birth that is not medical in any way.