Falsework refers to temporary structures used in the construction to support arched structures and concrete forms (moulds) in order to hold the component in place until its construction is sufficiently far advanced to support itself.
Formwork is made of panels and accessories that act as a mold to form a desired shape with concrete (for any purpose), Falsework is the temporary support structure for the forms.
Hardie G.M. (1995) Building Construction Principals, Practices, and Materials. New Jersey: Prentice Hall. (Pg 116, paragraph 1)