-RE is the receiver enable control. When low the receiver output is enabled and data appears on RO.
DE is the driver enable control, when high the DI signal is sent to the line, when low, the driver outputs are disabled.
The polarities are opposites simply to make it easier to use, they can be linked if necessary and then used as a single transmit/receive signal.
The first circuit uses switch S6 to pull the control line to +5V, which would make the transmitter active but the design is bad, when the switch is open there is nothing to pull the voltage low again. The diode should really be a pull-down resistor.
Brian.