Emuna is the guideline, while bitachon is putting that awareness into action.
Emuna is like a tree and bitachon is similar to the fruit. The fruit is a sign of the tree [that it exists]. However, the tree is not a sign of the fruit since there are trees that do not bear fruit. Yet, there is no fruit without a tree. ~ Ramban
One with bitachon not only believes Hashem runs the world, but acts in conformance with that belief. ~ Praying with Fire 2