Q: Why can't someone receive my texts when it says "Delivered" ?

Why can't someone (my sister) receive my texts when it says "Delivered"?  I can't receive hers either.  It's only one person who is not getting my texts even though it says "Delivered."  Also, they are all in blue, not green though I don't see how that can make a difference since other people get my texts and they are also in blue, sometimes green.  (Not sure I understand that whole blue, green thing anyway.)

She has a new iphone 6, I have a 5s though that shouldn't make a difference.  I just turned on my SMS option in my Settings but that didn't make a difference. By the way, should I have the SMS option ON or OFF as a rule?  It was in OFF position but it was never an issue before this.  Will I get charged if it's in SMS mode?  I have an unlimited text plan.

I would like to be able to text my sister...rather important!