Murder vs. Right to choose

I don't usually post topics like this...but this particular one has been weighing on me big time lately for some reason.  

I guess I just really do not understand the logic/inconsistency behind some of our laws.  

I'm not going to get all in depth and go off completely on this (well, maybe I will...not making any promises), but I just have to pose the question:

What is it that makes the difference between murder and the right to choose? Is it weeks?  Days? Physically being a living breathing creature that is no longer sustained by its "host"? 

Whatever the answer is for you - does it answer the following question?  

If a woman finds out she is going to have a baby who would be less than perfect and chooses to have a late stage (third trimester) abortion.  The child is alive right?  It moves, it kicks, it hiccups, it's heart beats.  Is this murder?

Okay, so now let's say this abortion fails.  The baby is born - now it is premature in addition to its other problems and very much unwanted by the parents who had chosen to terminate it.  So the baby is alive, breathing - but struggling.  The baby is carried off to a room where it is left to die.  Sometimes given the courtesy of a nurse or tech who will hold it till it dies, other times just left on a cold table to die by itself.  No medical intervention is given to this child that was born - entered the world - alive!  Is this murder?  

What about the woman or teenager who has a baby but gets scared or decides she can't deal with it so she abandons the newborn baby that is only minutes or hours old.  Perhaps she leaves it in a field...or in a trash can.  The newborn baby dies.  Is this murder?  If so, how is it different than the act above with the same outcome of a child the same age?

What about the mother of the two year old who is throwing temper tantrums every day...she just can't deal with it anymore so she terminates her childs life.  Is this murder?  

What about the mother of a teenager who is doing drugs and living a destructive lifestyle?  Or maybe just being an ungrateful brat?  She terminates that teenagers life.  Is that murder? 

My point is: what exactly is the point, the defining moment when we decide a life being terminated is murder vs the woman's right to choose?  Isn't terminating a teenagers life still the woman's "right to choose"?  I mean if our laws make it clear that a beating heart isn't the defining factor why is that not a woman's "right to choose?"  Apparently it isn't even that having breathed their first breath is the defining factor.  So where exactly is that distinction?  Is it minutes, hours, weeks after a child is born that we decide it's suddenly a living human worthy of living?  Is it okay to terminate a life that is an hour old because a woman decided while she was pregnant that she didn't want the child to be born?  So why not then when that child is 15 - using the same argument?

I guess I just don't understand - how can we prosecute the woman who throws her 1 hour old baby into a trash can, but not prosecute the woman or doctors who allow a child who was born from a failed abortion as being murderers but instead PROTECT them from prosecution.  

I don't get it...I guess I never will.