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A flow chart details the processes to follow. A DFD details the flow of data through a system.
In a flow chart, the arrows represent transfer of control (not data) between elements and the elements are instructions or decision (or I/O, etc).
In a DFD, the arrows are actually data transfer between the elements, which are themselves parts of a system.
Wikipedia has a good article on DFDs here.
Data flow diagram shows the flow of data between the different entities and datastores in a system while a flow chart shows the steps involved to carried out a task. In a sense, data flow diagram provides a very high level view of the system, while a flow chart is a lower level view (basically showing the algorithm).
Whether you use data flow diagram or flow charts depends on figuring out what is it that you are trying to show.
A Data Flow Diagram is functional relationship which includes input values and output values and internal data stored.
A Flow Chart is a process relationship which includes input and output values.