Dynamic Multi-Objective Optimization Problems (DMOPs) and Many-Objective Optimization Problems (MaOPs) are two classes of the optimization field that have potential applications in engineering. Modified Multi-Objective Evolutionary Algorithms hybrid approaches seem to be suitable to effectively deal with such problems. However, the standard Crow Search Algorithm has not been considered for either DMOPs or MaOPs to date. This paper proposes a Distributed Bi-behaviors Crow 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. Two variants of the proposed DB-CSA approach are developed: the first variant is used to solve a set of MaOPs with 2, 3, 5, 7, 8, 10,15 objectives, and the second aims to solve several types of DMOPs with different time-varying Pareto optimal sets and a Pareto optimal front. The second variant of DB-CSA algorithm (DB-CSA-II) is proposed to solve DMOPs, including a dynamic optimization process to effectively detect and react to the dynamic change. The Inverted General Distance, the Mean Inverted General Distance and the Hypervolume Difference are the main measurement metrics used to compare the DB-CSA approach to the state-of-the-art MOEAs. The Taguchi method has been used to manage the meta-parameters of the DB-CSA algorithm. All quantitative results are analyzed using the non-parametric Wilcoxon signed rank test with 0.05 significance level, which validated the efficiency of the proposed method for solving 44 test beds (21 DMOPs and 23 MaOPS).