The Camille Ring shows a bezel set center diamond. A bezel setting means there's a wall of metal holding the stone in place. It's the most secure setting because there's a solid wall of metal supporting and hugging the stone.
The Alyssa Ring shows a round diamond with four prongs. This style of setting is often referred to as a four-prong box. There's less metal here, so more of the focus is on the center stone. Variations on this style can have six prongs, eight prongs, etc.
Four-Prong Setting Oval with Halo
The Eliza Ring shows an oval diamond set with four prongs, but this time with a halo surrounding the stone. The halo really changes the look of a ring, right?
The Lillian Ring shows a more vintage style. There are eight tiny prongs on a flat surface of metal. This style is often referred to as an illusion plate or a miracle head, because it's designed to make your stone look larger than it actually is.