Imitation = fake = faux = simulated-- All these terms mean the pearls are man-made in factories. Most have glass beads inside; really cheap ones have plastic beads; some even have shell beads.
Cultured = farmed pearls. A nucleus of either tissue or a bead + tissue is surgically placed inside the mussel or oyster to stimulate it to lay down nacre over the nucleus.
Natural = wild pearls that formed in nature, without human intervention.
However, you didn't tell me whether you had tried rubbing them gently against each other? Remember I am only looking at photos while you have them in front of you. Gritty feeling = genuine nacre (usually); smooth feeling = imitation (usually). I say usually because grime can make the pearls stick a bit when rubbing, and if real pearls have been coated or polished they can feel smooth. For the brooches you can rub the pearl gently against the edge of your top front tooth. Don't rub hard or you may scratch the pearls.