Both faults are ordinary and expected — the difference is cost. A minor fault only needs a mapping fixed up for a page already in memory, taking microseconds. A major fault has to fetch from disk or swap, taking orders of magnitude longer, so a rising major fault rate is a direct latency signal. Touching an unmapped address is a segmentation fault, a different event entirely, and that is also the option describing process death. Both kinds occur in user and kernel context alike.
Official docs