Different physiological traits have been proposed as key traits associated with yield potential as well as performance under water stress. The aim of this paper is to examine the genotypic variability of leaf chlorophyll, stem water-soluble carbohydrate content and carbon isotope discrimination (Δ13C), and their relationship with grain yield (GY) and other agronomical traits, under contrasting water conditions in a Mediterranean environment. The study was performed on a large collection of 384 wheat genotypes grown under water stress (WS, rainfed), mild water stress (MWS, deficit irrigation), and full irrigation (FI). The average GY of two growing seasons was 2.4, 4.8, and 8.9 Mg ha−1 under WS, MWS, and FI, respectively. Chlorophyll content at anthesis was positively correlated with GY (except under FI in 2011) and the agronomical components kernels per spike (KS) and thousand kernel weight (TKW). The WSC content at anthesis (WSCCa) was negatively correlated with spikes per square meter (SM2), but positively correlated with KS and TKW under WS and FI conditions. As a consequence, the relationships between WSCCa with GY were low or not significant. Therefore, selecting for high stem WSC would not necessary lead to genotypes of GY potential. The relationship between Δ13C and GY was positive under FI and MWS but negative under severe WS (in 2011), indicating higher water use under yield potential and MWS conditions.