They are close but not the same. An enlisted guy can have more than one NEC but an officer will have only one designator.Enlisted have designators, too (NEC codes), um...sir.
Designator = warfare specialty. For example, 1320 = NFO. P-3, F-18, EA-6B, etc. NFOs all have the same 1320 designator.
NEC = specific qualification within their specialty (rate). For example, AWs. A P-3 SS1 has a different NEC than a P-3 SS3. But an AW can hold both NECs.