Today we're moving from the diamonds themselves to the way they are set. Above is a graphic showing twelve common ways stones (not just diamonds) can be set, in this case, all in eternity style bands. All the diamonds in this graphic are round brilliant, also referred to as full cut, but most other shapes can also be set in any of these styles.
The most common is the first in the graphic, the shared prong. As you can see, the prongs are between the stones, cut on both sides to hold the diamond.
French pavé has a V-shaped groove cut into the band, showing the diamonds from the side.
Bezel setting surrounds the diamond with a rim of metal. The graphic calls it a rubover, but I would just call it high polish.
Flush setting is when the diamonds are set so the crown (top half) of the stone is flush with the surface of the ring. The alternative name of Gypsy is outdated, but you may see it on an appraisal or description.
Scallop setting allows the edges of the diamonds to extend over the side of the metal to appear, well, scalloped.
Channel setting is when the diamonds are slotted between two edges of metal. This is a low maintenance setting style.
Pavé is from the French word for paved and is pronounced paw-vay. This is the term for rows of small diamonds set with tiny beads raised between the stones to hold them in place.
Fishtail is an older setting style, very similar to French pavé.
Milgrain is the term for the beaded edges shown on this bezel set band. You can also see milgrain detailing on channel edges or on vintage and vintage-style pieces.
Bar setting is just that-- bars between the stones. You often see bar setting with baguettes.
Prong setting is very common and is different from shared prong in that each stone is held in place with its own set of prongs instead of sharing with the stone next to it.
The final style in the graphic is called "floating" but is often referred to as single-prong. The stones are cupped by metal with just a single prong between them. This is pretty but not necessarily durable.
I hope this little crash course in setting styles is helpful, and as always, feel free to ask any questions you may have.