Differences among different sieves encountered in sieve theory Are the sieve techniques used in understanding the twin prime conjecture or other number theoretical conjectures different from sieve theory used in primality testing or integer factorization? What are the differences between different sieve techniques? Could someone explain at a high level?

I don't know what a high level is.

I would say that the difference is operational. The sieves in factorization (quadratic sieve, number field sieve) are algorithmic techniques designed to optimize computations. The sieve in analytic number theory are theoretical constructs designed to optimize estimates of the number of elements in various sets.