The aim of this work is to compare two existing multilevel computational approaches coming from two different families of multiscale methods in a nonlinear solid mechanics framework. A locally adaptive multigrid method and a numerical homogenization technique are considered. Both classes of methods aim to enrich a global model representing the structure’s behavior with more sophisticated local models depicting fine localized phenomena. It is clearly shown that even being developed with different vocations, such approaches reveal several common features. The main conceptual difference relying on the scale separation condition has finally a limited influence on the algorithmic aspects. Hence, this comparison enables to highlight a unified framework for multiscale coupling methods.