So with NH2(-) and C2H (-), the former is more basic despite the charge being on the more electronegative atom (N > C) because the negative charge on the latter terminal alkyne is stablized by the sp orbital (triple bond), making it a weaker base. The NH2 would hold the basic electrons tighter due to Nitrogen being more electronegative, but it turns out the tight bonding (sp orbital) holds the basic electrons on C2H even tighter. So the net result is NH2 basic electrons being held more loose than those of C2H. However, it does not apply to all Ns and Cs. A CH2 (-) would be more basic than NH2(-). The previous two are exceptions for a reason.
Hope that helped!