Dynamic multi-objective optimization problems (DMOPs) and Many-Objective Optimization Problems (MaOPs) are two classes of the optimization filed which have potential applications in engineering. Modified Multi-Objective Evolutionary Algorithms hybrid approaches seem to be suitable to effectively deal with such problems. However, the Crow Search Algorithm has not yet considered for both DMOP and MaOP. This paper proposes a Distributed Bi-behaviorsCrow Search Algorithm (DB-CSA) with two different mechanisms, one corresponding to the search behavior and another to the exploitative behavior with a dynamic switch mechanism. The bi-behaviors CSA chasing profile is defined based on a large Gaussian-like Beta-1 function which ensures diversity enhancement, while the narrow Gaussian Beta-2 function is used to improve the solution tuning and convergence behavior. The DB-CSA approach is developed to solve several types of DMOPs and a set of MaOPs with 2, 3, 5, 7, 8, 10 and 15 objectives. The Inverted General Distance, the Mean Inverted General Distance and the Hypervolume Difference are the main measurement metrics are used to compare the DB-CSA approach to the state-of-the-art MOEAs. All quantitative results are analyzed using the nonparametric Wilcoxon signed rank test with 0.05 significance level which proving the efficiency of the proposed method for solving both 44 DMOPs and MaOPs utilized.