Not everyone with insomnia suffers from anxiety as well, and neither the reverse, but they're not two completely unrelated disorders/diseases either.
Some might say that anxiety isn't even a disorder or an abnormality, but just a symptom of living a human life that everyone has to deal with.
I don't buy into that.
It might not always be bad to be something other than "normal", but I think we should call it what it is.
No one wants to sweat (especially when they're not exercising) and no one wants to breathe in and out of a paper bag.
And the fact is that if you relieve yourself of anxiety and stress, insomnia may follow.
For me that was almost exactly the case.
Once I stopped worrying about the exam I had the next day or whether I should have said/did this or that during the previous day, my nights have been far more sleep-enriched.
I started spending less hour awake in my bed thinking about usually the most mundane and futile things and more timesleeping! Remember, your bed is for sleeping.
Behaviourist psychologists and sleep therapists all agree that if your bed is associated with anything other than sleep, you'll probably end up using it for everything, except sleep.
It's very important to condition yourself to viewing your bed or wherever you like to sleep as just that, and nothing else.
This will result in you viewing your bed as a place for rest, and your body will respond.