Quartzes

Quartzes are a broad collection of Gems cuts that serve as the primary soldiers of Homeworld's Caste System. Some Quartzes are higher ranking than others, being described as "elite" or holding commander positions while the majority maintains a common soldier ranking.

Role
Quartzes are a soldier caste. Some Quartzes are used as bodyguards and escorts as shown in Jasper's case. They appear to be less numerous than Rubies. According to Ian Jones-Quartey, some have defensive powers as well (like Rose's) since "they can't all be tanks." Jasper stated that Quartzes are made to fight and Jaspers specifically always get what they want. Some also act as guards at Homeworld outposts such as Pink Diamond's zoo. They were commonly made on Earth. Quartzes are the most diverse known Gem type with Gems including Amethysts, Carnelians, Jaspers and Rose Quartzes.

Other Quartz types include Agates, who rank higher and seem to be administrative in nature and Citrines, who seem to be elite guards (including Emerald and Hessonite's guards).

Physical Characteristics
Quarztes are much larger than most other types of gems, made to fit the role of an elite warrior, Quartzes have incredible height, broad shoulders, and an intimidating muscular build. While their exact height can vary depending on how well they formed when they were incubating in the ground, most quartzes appear to be the same height as each other, with variations of this standard height being very rare. Quartzes (excluding Agates) have some of the longest and thickest hair of any gem. Their hair colour is often a very pale tone of the colour of their gem, although some have dark brown hair.

All Homeworld Quartzes wear the standard Homeworld uniform, while quartzes with a more managerial position, such as Agates, wear an additional shawl and boots. Decorated Quartzes, such as Jasper, can also wear a cape over their uniform, though this isn't actually a part of their physical form.

When Corrupted, Quartz gems take the form of a giant eyeless wolf-like beast. They have a furry mane which extends down their back and covers their tail, and they can have a number of horns on their head. They also develop patterns on their bodies resembling those found on their real-life Gemstones.

Agates
Agates hold a position of authority slightly higher than other Quartzes. They appear to serve as a form of manager for groups of other types of Quartzes, keeping them in line and ensuring that they perform their duties. So far, Holly Blue Agate is the only one of the Agates shown. She is in charge of a group of Quartz soldiers and manages Pink Diamond's Zoo. Other types of Agates have been mentioned such as:
 * Crazy Lace Agate - An Agate who was originally a member of the Crystal Gems.
 * Pink Diamond's Agates - Agates who used to belong to Pink Diamond, they were her bodyguards during the Rebellion, first mentioned by Blue Zircon in "The Trial".
 * Yellow Diamond's Agates - Agates who reside in one of Yellow Diamond's Asteroid Mines and first mentioned by Rhodonite in "Your Mother and Mine".
 * Unknown Holly Blue Agate - A Holly Blue Agate seen watching Steven's message in an unknown gem city. Her gem is located on her lower back.

Amethysts
Amethysts are a purple type of Quartz, most notably produced on Earth's Prime Kindergarten for Pink Diamond. Besides Amethyst 8XM, the Amethysts from Earth were stationed at Pink Diamond's Zoo thousands of years later, now serving Blue Diamond and are commanded by Holly Blue Agate due to the "shattering" of Pink. Like Amethyst 8XM, these Amethysts share a laid back and comedic personality.

History
Four Amethysts appear in "Gem Heist" at Pink Diamond's Zoo; two of them are in charge of guarding the door in the Zoo's cargo bay. The two Amethysts tease the Crystal Gems when they land on the Zoo, resulting in a scolding from Holly Blue Agate. Later in "Gem Heist," another pair of Amethysts send Steven into the Zoo's tunnel, one with a square-faceted gemstone.

In "The Zoo," several Amethysts are seen entering the boundaries of Pink Diamond's Zoo to console the heartbroken Zoomans. One Amethyst later angrily informs Greg and Steven of the trouble they are in.

In "That Will Be All", this turns out to be a prank by Amethyst and the many other Homeworld Quartz guards she has met (whom she refers to collectively as "the Famethyst"), three of which having been formed right above her. These Amethysts inform her of her serial number being Facet-5 Cut-8XM. Among the Amethysts and Jaspers are two defective Gems: "Skinny", a tall and skinny Jasper, and Carnelian, shorter than most Quartzes.

In "Now We're Only Falling Apart", numerous Amethysts are shown emerging out of the Prime Kindergarten in a flashback from Pearl.

In "Together Alone", several Amethysts and Jaspers are shown in the crowd of Quartz Gems dancing alongside the Crystal Gems' Amethyst during the Era 3 Ball.

"Now We're Only Falling Apart"
Many Amethysts appear in Pearl's flashback, all of which emerging from the Prime Kindergarten.

"Together Alone"
Several Amethysts attend the Era 3 ball, seen dancing along with several Jaspers.

The Phantom Fable
They appear in Delta Kindergarten. They are all enemies.

Jaspers
Jaspers are a broad variety of Quartz soldiers that vary in color, such as Biggs Jasper and the Snow Monster. The famous Jasper describes her cut as never giving up and always getting what they want.

"That Will Be All"
Several Jaspers from the Beta Kindergarten debuted in That Will Be All. Like the Amethysts, they originally belonged to Pink Diamond but now served Blue. Despite their Gem type, they are all considered members of The Famethyst.

"Together Alone"
Two identical Jaspers attend the Era 3 ball, seen dancing along with several Amethysts .

The Phantom Fable
She appears in Delta Kindergarten.

Carnelians
Carnelians are a red type of Quartz, most notably the defective Carnelian from the Beta Kindergarten.

Rose Quartzes
Rose Quartzes are a pink type of Quartz.

"That Will Be All"
Steven and his father Greg saw the bubbled Rose Quartz Gems in Pink Diamond's Zoo.

"The Trial"
They were mentioned by defending Zircon that there's no Rose Quartz soldiers in Pink's entourage.

Citrines
Citrines are a yellow type of Quartz who seem to be an elite caste of guards serving high-ranking Gems.

Tiger's Eyes
Tiger's eyes are a type of Quartz which is yet to be seen but has been mentioned by name.

Quartzes in "Your Mother and Mine"
These Unknown Quartzes appear in "Your Mother and Mine".

Quartzes in "Change Your Mind"
Six unknown types of Quartz Gems can be seen in Rose's Fountain after having been healed from corruption. They all have different colors, skin patterns, and horns on their heads which they retained from when they were corrupted. They too appears in "Steven Universe: The Movie".

Steven Universe: The Movie
Four unknown quartzes can be seen from behind watching Steven's message.

Unknown Blue Quartzes
These gems appear in The Phantom Fable. Their weapons are large tipped spears.

Trivia

 * All Amethysts are voiced by Michaela Dietz (who voices the Crystal Gems' Amethyst); all Jaspers and the defective Carnelian are voiced by Kimberly Brooks (who also voices Jasper).
 * So far, it is true that Gems of the same gemstone (with the exception of the Diamonds) also share the same voice, albeit with some differences in tone. Their appearances are also nearly identical, excluding gemstone placement and details such as hair length and style, skin tone and patterning in the case of Jaspers.
 * Both Carnelian and "Skinny" are voiced by Kimberly Brooks despite being two different types of quartz, suggesting different Gems may share the same voice actor.
 * So far, Jaspers are the only type of Quartz who are shown to normally have patterns on their skin, although all quartzes have patterns when corrupted.