Flux means flow, and is used in astrophysics regarding electromagnetic radiation (EMR) (e.g., the flow of its energy), magnetic fields, fluid dynamics, and other areas.
Flux density (often shortened to flux) is the rate of flow of something through a unit area. However, the term flux is also used to mean the total flow rate from something, e.g., the phrase radiant flux being the total flow of EMR energy to/from/through something (a star's radiant flux would be its luminosity). The term flux is also used regarding CCDs, to refer to the rate of EMR reception by a defined portion of it, such as that received by an individual pixel.
Fluence (aka radiant exposure, in the case of EMR) is a total amount of flow per unit area rather than a rate. For example, the fluence of a gamma-ray burst indicates the total energy it put on each cm2 over the course of the entire burst (whereas the burst's flux density at some point in time would indicate the rate at which it was putting energy on each cm2 at that point in time).