What is the difference between reliability and integrity?

In functional safety, ‘reliability’ is a mathematical term expressing the probability that the SIF has not suffered a random hardware failure.
However, control of systematic failures is also necessary. The term ‘integrity’ expresses the degree of confidence that both random and systematic failures are adequately controlled. Thus, the term ‘SIL’ (safety integrity level) implies attention to all aspects of the functional safety lifecycle.

Reference: Functional Safety from Scratch by Peter Clarke, xSeriCon