Formwork is best described as “A structure which is usually temporary but can be whole or part permanent, it is used to contain poured concrete to mould it into required dimensions and support until it is able to support itself.” (you can find in Xingtai Horizon Formwork--"Table formwork system"and "Wall and Column formwork")
There have been numerous developments for further reading with regards to formwork, one of which began the theory of formwork was; Formwork – a guide to good practice, published by the Concrete Society and Institution of Structural Engineers in 1995. This volume embraced the various aspects of Formwork, which included, design, materials, equipment, site best practice and special Formwork.
Falsework is described as “A temporary structure used to support a permanent structure during the erection until it becomes self supporting.” However, this can sometimes be misinterpreted as it could be read to include horizontal and raking supports. Research of the code of practice states that Falsework is when dealing with situations where the supporting systems is carrying a vertical load. A better definition could be, “Falsework is any temporary structure, in which the main load bearing members are vertical, used to support permanent structures, used to support a permanent structure and associated elements during the erection until it is self supporting.”
Given the two definitions of Formwork and Falsework they are given strict boundaries between the two, there are occasions when Formwork and Falsework become combined in methods which go by the names of Table Forms and Flying Forms. (you can find in Xingtai Horizon Formwork--"Table formwork system")