Emunah (faith, or belief) and Bitachon (trust, or reliance) are closely related ideas, but Emunah is conceptual, whereas Bitachon is practical.

A person with Emunah knows in his mind and believes in his heart that Hashem can provide for all his needs, but has not necessarily applied that faith in actual practice.

A person with Bitachon, however, leads his life in accordance with the knowledge and belief that Hashem provides for him.

~ Artscroll introduction to Shaar Habitachon