The refelxity is a technical condition that ensures the existence of utility function. It is an axiom.
While local non-satiation is an assumption, which is one of the conditions of first and second welfare theorem.
And anothing needs to be pointed out here is that, local-nonsatiation does nor mean the more the better, it just means that in any neighbourhood of a consumption bundle, there is other consumption bundle which is prefered to the original one. While the more the better means monotonicity, which is stronger than local non-satiation.