Is the EXTD_EN pin in ADGM1004 and SLEEP pin in ADGM1304 have the same functionality of putting the IC in sleep mode?.
ADGM1004 doesn't have sleep function. In ADGM1004 when you set EXTD_EN high, the device goes to low power mode consuming only 50uA current (max). In this mode oscillator and charge pump circuitry will be disabled. With the oscillator disabled, the MEMS switch can still be controlled via the logic interface pins (IN1 to IN4), but the VCP pin must be driven with 80 V dc from an external voltage supply.
ADGM1304 does have sleep pin, when you set the sleep pin high the device goes to sleep mode consuming only 1uA current.