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