Background: Salt stress is a multicomponent phenomenon; it includes many processes that directly or indirectly affect the plant. Attempts have been made to comprehensively consider the processes of salt stress in plants Triticum aestivum (variety Orenburgskaya 22) and Triticum durum (variety Zolotaya). Methods: The study used methods of light and fluorescence microscopy, methods of immunofluorodetection, expression of DNA methyltransferase genes, genes of the ion transporter and superoxide dismutase families, as well as biochemical determination of total antioxidant activity using the 2,2-diphenyl-1-picrylhydrazyl (DPPH) reagent. Results: According to morphometric indicators, the Orenburgskaya 22 variety showed greater tolerance to the action of 150 mM NaCl than the Zolotaya variety. The level of expression of genes of the HKT ion transporter family in the Orenburgskaya 22 variety is higher than in the Zolotaya variety. It was found that the expression of the DNA methyltransferase gene DRM2.1, which post-translationally methylates cytosine residues, is 22.3 times higher in Zolotaya compared to Orenburg 22 when exposed to salt. The accumulation of toxic ions is accompanied by an increase in reactive oxygen species (ROS) and increased damage to root tissue, especially in the Zolotaya variety. Using fluorescence microscopy using the Carboxy-H2DFF marker in the Orenburgskaya 22 variety at high NaCl concentrations, the highest fluorescence intensity was determined in the cap zone; in the Zolotaya variety—in the zones of the cap and root meristem. Excess ROS is more successfully removed in the Orenburgskaya 22 variety, which has a higher level of antioxidant activity (AOA), as well as the level of expression of the Cu/ZnSOD and MnSOD superoxide dismutase genes. Using programmed cell death (PCD) markers based on the release of cytochrome c from mitochondria into the cytoplasm, DNA breakage and the release of phosphatidylserine from mitochondria, the degree of damage to root cells was assessed in both wheat varieties. It has been proven that wheat cell death occurs through the mitochondrial pathway. It was noted that the salt-sensitive variety Zolotaya had a significant number of necrotic cells. Conclusion: Based on the data obtained, it was concluded that the Orenburgskaya 22 variety exhibits greater resistance to salinity than the Zolotaya variety. These data may be of practical importance for enhancing protective mechanisms under abiotic stress.