The colored stones in your clasp appear to be pinkish rubies. Please note that unmarked gold is extremely common, depending on country of origin and time period. For example, gold marks were not legally required in the U.S. until about 1908. The clasp looks well-made, so you could have it tested to determine gold content.
If you are getting that 'gritty' feeling to the teeth with both necklaces, I would say the first one appears to be cultured saltwater pearls, and the second one may be inexpensive freshwater pearls. The clasp on the second is costume jewelry, but I agree with those who note that clasps can always be changed -- I have run into many examples of that myself.
The Pearl of Great Price was not something farmed by Mikimoto