The production of potato (Solanum tuberosum L.) faces a severe challenge due to the salinization of arable land worldwide. The cultivation of salt-tolerant potatoes is of great significance to ensure food security. In this study, two cultivars of ‘Longshu 5’ and ‘Qingshu 9’ were compared for physiological responses to salt stress, and then the salt tolerance of the two cultivars were assessed via principal component analysis. Furthermore, the Na+, K+, and Ca2+ flux of the cultivars under salt stress was recorded. Finally, the expression levels of ion transport-related genes and transcription factors in salt-tolerant cultivars were explored under NaCl stress. The results showed that the seven physiological indicators of salt tolerance were differed between the cultivars. Interestingly, soluble protein and sugar were early responsive to salt stress than proline in the salt-tolerance cultivar. Peroxidase and superoxide dismutase activity were significantly different in ‘Longshu 5’ under NaCl stress and without being significantly different in ‘Qingshu9’. In addition, the salt tolerance of ‘Longshu 5’ was more tolerant than ‘Qingshu 9’ based on principal component evaluation. Meanwhile, the strong efflux of Na+, the stability of K+, and the high absorption of Ca2+ in ‘Longshu 5’ indicated salt adaption mechanisms in the salt-tolerant potato. In addition, we found that ion transport-related genes and transcription factors, such as StSOS1, StNHX4, StAKT1, StNAC24, and StCYP707A, played a role in the salt tolerance of ‘Longshu 5’. In conclusion, the salt-tolerant potato can regulate physiological substances to adapt to salt stress, and ion transport related genes and transcription factors play a role in improving salt tolerance.