What is the difference between predator plants and parasite plants?

A parasitic plant is a plant that depends on the nourishment of another plant and in the process harms the plant it nourishes, i.e. the host plant.

Predatory plants differ in two broad senses:

They don’t depend on plants. They depend on insects.
Unlike parasitic plants, they are capable of photosynthesis. The insects they hunt are like dietary supplements in that they grow in soils that are lacking in important nutrients such as nitrogen for protein synthesis.