The apricot storability is one of the largest challenges, which the apricot industry has to face all over the world; therefore, finding options for prolonging fruit quality during cold storage (CS) and shelf-life (SL) will help to decrease postharvest losses of apricot. The aim of this apricot fruit work was to study the temporal changes and correlations of 10 quality parameters (quality losses, antioxidant properties and enzyme activities) in the postharvest treatments of methyl jasmonate (MeJA) and salicylic acid (SA) under 1 °C CS (7, 14 and 21 days) and 25 °C SL (4 and 8 days after the 21-day CS) treatments. MeJA and SA significantly decreased the quality loss of chilling injury (CI) and fruit decay (FD) at all dates for both storage conditions. MeJA- and SA-treated fruits increased total antioxidant capacity (TAC), total soluble phenolic compounds (TSPC) and carotenoids contents (TCC) at all dates of both storage treatments. In contrast, the ascorbic acid content (AAC) increased only until days 14 and 4 in the CS and SL treatments, respectively. Among enzyme activity parameters, the activities of phenylalanine ammonia-lyase (PAL), peroxidase and superoxide dismutase (SOD) were significantly increased in the MeJA and SA treatments in all dates of both storage treatments. Catalase (CAT) activity increased in the SA and control treatments, while it decreased in the MeJA treatment in both storage conditions. In both the MeJA and the SA treatments, six pair-variables (FD vs. CI, PAL vs. CAT, PAL vs. SOD, TAC vs. SOD, TAC vs. FD, and AAC vs. CI) were significant in Pearson correlation and regression analyses among the 45 parameters pairs. Principal component analyses explained 89.3% of the total variance and PC1 accounted for 55.6% of the variance and correlated with the CI, FD, TAC, TSPC, TCC, PAL and SOD, indicating strong connections among most parameters. In conclusion, MeJA and SA are practically useful and inexpensive techniques to maintain quality attributes of CI, FD, TAC, TSPC, TCC, PAL, POD and SOD in apricot fruit during both CS and SL conditions.