not quite, a wastegate releases excess exhaust gases from the turbine side when the desired boost pressure has been reached to ensure the turbo doesnt keep compressing the air and boost higher than you want it to.
a dump valve/recirc valve releases pressure from the compressor side that becomes trapped in the pipework when the throttle body shuts, otherwise air will travel back over the compressor blades causing the turbo to stall and hence take longer to spool up after a gear change. This also makes the flutter noise or 'pigeon dump' that people often attribute to the wastegate.