On Piping & Instrumentation diagrams (P & ID) the flow element - FE (or flow meter) is the physical item on the pipe which measures the flow. It could be an orifice plate, or other device.
The Flow Indicator - FI -would be the gauge on the meter, which is mounted locally to read the flow. If the flow is to be read remotely, as in a control console, a flow transmitter - FT - would be needed to transmit the data. So you will often see the grouping - FE, FT, FI - on the P & ID.