Measurement gaps are required to measure the RSRP of the inter frequency/IRAT neighbors. This is required because UE needs to switch their RF receiver from current frequency to the neighbor inter frequency/IRAT frequency and then need to read the RSRP of the these cells. For intra frequency RSRP measurement measurement gap does not required. UE can measure RSRP of same intra frequency neighbors without measurement gaps as this is not require the to UE to switch their RF to the other frequency.
DRX gap can vary in time but measurement gap is fixed of 6 ms. Drx gaps are used to save the UE battery or to read the ECGI of the neighbor cell.