There is definitely a relationship between the two.  If you were completely secure you would not need to worry. 
The question is,  since none of us as humans are ever completely secure, why do some people worry and others don't?  I imagine it's learned at childhood, both through worrisome events, and as modeled by one's parents/caregivers.

There is an old German joke about the difference between a Prussian officer and a Bavarian one reporting to their general.  The Prussian goes "The situation is desperate, but not hopeless", whereas the Bavarian will say "So the situation is hopeless - but not desperate". 

Rachel - I also worry too much.  I missed the Bavarian mindset by about 300km.  For me it helps to think things through.  Sometimes thoroughly fantasizing through the worst case scenario puts things in proportion.  When I don't have the time to think, I worry more.  It seems I need to have a sense of clarity, some idea of what's coming at me.  I suppose on a deep level the worry is about my capacity to deal with what comes and survive.  When I think through the worst case scenarios I always eventually get to death, and that doesn't seem so bad.  From what I remember from before I was born in was dark and quiet and peaceful. 

I honestly believe over-thinking has got me to this, I understand that for you thinking it thoroughly helps, but to me - it feels like I go in a circle, and yes, death comes, but I do not want that. So my mind plays it again. Hm, I will make a conscious effort to try everything and anything I can to let the person know I care - I should be happy with that. It will be a process, a hard one, but in the end I can only control myself, so for instance seeing a close friend -on his bike- going over 100mph in heavy traffic is terrible, but I can just not let it always be on my mind. Peoples acts, or words, I simply cannot let it rule me. I am an individual with needs as well, and living with my mind being consumed with thoughts of others simply won't work. I want to stress consume, because I understand it is human to think, and care for others, but you need time for yourself, and always time to step away and reflect.Thank you for your thoughts Rhea.

Ahh - I didn't realize it was another person you worry about. 
The process of thinking it through does not work the same way in that case. 
I am quite alright with my own demise, but when I worry about my daughter for example, that worst case scenario will not be comforting.  I get angry at her, and then I need to explain to her that it's because I'd be devastated if anything bad were to happen to her. 
When you care about someone, you need to let them know when their behaviour concerns you.  They should know that their safety and well-being is important to someone.  Just as long as you're clear that adults do whatever they feel like with that info.  If hurtling through traffic or solo glacier skiing is part of their identity, then your worry may feel like a burden or annoyance. 
And yes, when worrying about people it's probably best to stop thinking altogether, since there is nothing one can ultimately do about their behaviours.  Perhaps in that case, something like faith works better than thinking.