Hi there,
Critical update
A widely released fix for a specific problem that addresses a critical, non-security-related bug.Security update
A widely released fix for a product-specific, security-related vulnerability. Security vulnerabilities are rated by their severity. The severity rating is indicated in the Microsoft security bulletin as critical, important, moderate, or low.
Actually, both of them are recommended to be installed as soon as possible (I would prefer to say immediately)
Both of them could impact on your applications, but in this case, you need to leverage BCDR practice as well, which is mostly a customer's responsibility.