We demonstrate that the recently proposed soft gluon factorization(SGF)is equivalent to the nonrelativ-istic QCD(NRQCD)factorization for heavy quarkonium production or decay,which means that,for any given pro-cess,these two factorization theories are either both valid or both violated.We use two methods to arrive at this con-clusion.In the first method,we apply the two factorization theories to the physical process J/ψ → e+e-.Our expli-cit calculation shows that both SGF and NRQCD can correctly reproduce the low energy physics of full QCD,and the two factorizations are thus equivalent.In the second method,by using equations of motion,we successfully de-duce SGF from NRQCD effective field theory.By identifying SGF with NRQCD factorization,we establish rela-tions between the two factorization theories and prove the generalized Gremm-Kapustin relation as a byproduct.Compared with the NRQCD factorization,the advantage of SGF is that it resums the series of relativistic corrections originating from kinematic effects to all powers,yielding better convergence of the relativistic expansion.