I think we need times for both silence and stillness.
I consider silence as quiet time when we’re not on the go.
Throughout the day we occupy ourselves with work, phones, TV, people, and whatever else. We don’t have time to just sit and think so when we try to go to bed we just start thinking and won’t allow ourselves to wind down and fall asleep. I used to do this all the time, but I’ve gotten a little better lately.
If we allow ourselves a little space to think we may come up with great ideas. Have you ever had what seems like a brilliant idea at night when you were trying to sleep?
Stillness, the way I am using it here, means doing nothing on purpose. In fact, if thoughts come into our head we need to not indulge in them…even great ideas. We just have to let them go if we are trying to be still. This is practically painful at first but if we do it for a few minutes every day, in time we will find it gets easier and we can be calmer throughout the day.

There is a great book called Wherever You Go There You Are by Jon Kabat-Zinn to help achieve stillness. It has short mediations to help you learn to slow down. My favorite one is the following:
Breathing in: “I calm my mind”
Breathing out: “I am smiling”
Breathing in: “Present moment”
Breathing out: “Wonderful moment”
Practice this for 5, 10, 20 minutes daily and you will get there.
Did you ever read or see the movie Eat, Pray, Love and Ketut, the medicine man, tells Julia Robert’s character, Liz, to smile as her meditation? I always wondered how you just practice smiling, but I found this meditation helps with that.
When you realize your mind has wondered start thinking about your breath again and focus. I’ve found even when I’ve had sessions when my mind wondered the whole time I still feel calmer and focused throughout the day. I recommend this book highly.