This is a common question that has come up in my bookbinding workshops. Here is a quick explanation, as your intentions for your book can help dictate how you might want it to look.
BOOK OF SHADOWS
A BOS is basically a witch's journal. It is a private book that is usually for the owners eye's only, detailing all of their magical workings, correspondences, dreams, personal thoughts, feelings and interpretations. A witch may authorize someone else to see it, but it should be regarded as sacred, and kept protected.
A Grimoire is a more technical book. It contains magickal research such as spells, potions, rituals and the magickal properties of various things like stones, herbs and oils. This book is meant to be passed down throughout a witchcraft family over generations.
In general, it is more common for witches to keep a BOS, if they do not keep both. Having a record of your magickal workings will help you progress in your powers, by seeing what works and what doesn't work for you personally. However, keeping both books is a good idea, since you can take your Grimoire around with you and share your research, while keeping your Book of Shadows safe in it's hiding spot