The photos are a little out of focus but based on round shape, varied luster and overtones, and a few pearls with visible surface characteristics typical of real pearls they are likely
cultured akoya pearls (as opposed to imitation pearls).
They look nice!
See if the clasp/chain has a gold mark on it. Usually imitation strands don't have gold clasps.
Also, rub 2 of the pearls gently together or against the edge of one of your front teeth. If they feel a bit resistant or slightly gritty, that is how genuine nacre feels. If they glide very smoothly against each other or against your tooth with no resistance at all, they are likely imitation. (However coated real pearls may feel smooth and grimy imitation pearls may feel resistant.)
Imitation pearls also may have some or all of these characteristics (particularly cheaper pearls):
• extra swirls of build-up pearl-like coating near drill holes
• peeling coating that is very thin with the bead visible underneath
• beveled drill holes
• all the same size or shape, in the case of non-graduated strands (but some imitation strands have variable shapes and size pearls)
• all have the same overtones (usually none; Majorica brand have green and pink overtone colors due to the final layer of coating they receive).
• larger drill holes than real pearls have (pearls are sold by weight so drill holes are small)
• very cheap pearls with a plastic bead inside will be unusually lightweight; better imitations have glass beads and feel heavy, more like real pearls.
• glass bead imitation pearls may feel very slightly warmer against the skin than genuine pearls
• If you have a 10x loupe (magnifier), look at the surface. Real nacre looks very smooth, while imitation pearl coating looks coarser textured. If in doubt compare with known-real or known-fake pearls.
Most
freshwater pearls that are solid nacre are not fully round. The Chinese are now culturing smaller freshwater pearls with beads inside that are round, but they are not yet commonly found.
I hope this helps you figure out what other pearls you come across may be.
Post photos if not sure, though!