This study was conducted to identify physiological and morphological traits linked with drought tolerance and variation among different bread wheat genotypes. In this study, 20 different bread and durum wheat genotypes were characterized on morphological, biochemical, and physiological traits under well-watered (70% water holding capacity; WHC) and drought stress (35% WHC) conditions. Drought stress significantly affected different morphological, biochemical, and physiological traits of wheat; however, significant genotypic differences were noted in both bread and durum wheat genotypes. Under drought stress, the activities of catalase and superoxide dismutase were higher in all tested genotypes compared to well-watered conditions. Regarding physiological traits, an overall increase in the leaf temperature, SPAD chlorophyll contents, intercellular CO2 concentration (Ci), water use efficiency (WUE), intrinsic (WUEi), and instantaneous (WUEins) water use efficiencies was recorded across the genotypes under drought stress compared to well-watered conditions. The principal component analysis (PCA) showed that under drought stress, the two principal components (PCs) had a significant variation for morphological and biochemical traits and the contribution of variation was 39.1 and 25.6% by PC1 and PC2, respectively. For physiological traits, under drought, the PC1 contributed 59.2 and PC2 18.4% of the total variability and the Ci, SPAD chlorophyll contents, photosynthesis (A), WUE, WUEi, and WUEins were negatively correlated, while stomatal conductance (gs), transpiration rate (T), and the ratio of A/Ci were positively correlated with PC1. The genotypes SQU-97, SQU-95, and SQU-80 were grouped based on high Ci, A, WUE, WUEi, and WUEins, while genotypes SQU-85, SQU-86, SQU-89, and SQU-90 were grouped based on high gs, T, and A/Ci. The agglomerative hierarchical clustering clustered the studied genotypes into three classes and the variation within the classes was 47.6%, while between the classes was 52.4%. The wheat genotypes (SQU-79, SQU-82, SQU-87, SQU-89, SQU-91, SQU-93, SQU-94, SQU-95, SQU-96, and SQU-98) with higher SPAD chlorophyll contents, antioxidant activities, intercellular CO2 concentration, water use efficiencies, and net photosynthesis were better able to tolerate the drought stress.