Sensitivity provides information on how much amplification is needed so a mic can capture quiet sounds. Max SPL refers to the maximum sound pressure level (at a given frequency, usually 1kHz) the microphone can handle before it begins to distort the audio. Rarely will that SPL figure lead to a microphone breaking, though it’s possible.
To complicate it further, because max SPL figures listed are usually measured at the 1kHz frequency, a mic can distort at higher or lower SPL depending on the design of the mic at a different frequency than 1kHz. For instance, ribbon mics tend to distort at lower SPL readings than the max SPL specification with sources (bass drums, bass guitar) that produce lower frequencies than 1kHz.