For each Digimon story, there are a team of human children who bond with Digimon. All are led by a boy in goggles. They are referred to as either "DigiDestined" or "Tamers"

So what's the difference? Mostly it's metaphysical. Any Tamer can have a Digivice and Digimon partner, but only a DigiDestined has been specially selected to carry the power of a Sigil Artifact, such as Crest, a Digimental, or a Spirit. And the two are not always mutually exclusive: while Tai, Davis, and their teams are DigiDestined who are also Tamers,Willis and the kids seen around the world in "Digimon World Tour" would really be better classified as Tamers. Takato's team of course are Tamers; they aren't DigiDestined because they have no Sigil Artifacts (That doesn't make them any less important or powerful than a "real" DigiDestined.) Only the DigiDestined of Frontier aren't also Tamers (they don't have Digimon partners)

Crests
The original eight Crests were created, along with the eight prototype D-Zero Digivices, by the Sentries for the first team of DigiDestined. When placed in a focusing device called a Tag, the Crests would allow a DigiDestined to Digivolve his partner to Ultimate or even, though this only happened in two of the eight cases, Mega level.

The Crest of Courage was carried by Tai Kamiya
The Crest of Friendship was carried by Matt Ishida
The Crest of Love was carried by Sora Takenouchi
The Crest of Sincerity was carried by Mimi Tachikawa
The Crest of Knowledge was carried by Koushiro "Izzy" Izumi
The Crest of Reliability was carried by Joe Kido
The Crest of Hope was carried by Takeru Takaishi
The Crest of Light was carried by Kari Kamiya

Unfortunately, all eight of the original crests were destroyed by Apocalymon in 1999. By that time, the DigiDestined had internalized the energies to the point they could still trigger the Digivolutions--until the Sentry Gennai asked for them to forsake those powers, allowing him to reawaken the Digimon Sovereign.

A ninth crest was later revealed:
The Crest of Kindness was carried by Ken Ichijoji

However, the origins of this item remain sketchy. No accounts of the adventures of Kamiya's team in 1999 suggest a missing "Ninth Child", which hints that the Crest of Kindness was created later. Ichijoji never used the Crest's power to Digivolve Wormmon--possibly because he never had a Tag for it. Ichijoji didn't even realize he had it until it emerged from it's hiding place in his fortress's reactor.

(In Japan, the Crest of Sincerity was called Purity, and Reliabilty was known as Faith)

Digimentals
(Known as "Digi-Eggs" in the American dub)
The Digimentals are an ancient set of Sigil Artifacts, possibly the very first. They were reawakened in 2002 to combat the mad scheme of the "Digimon Emperor"; the Digimentals can trigger a unique form of Digivolution, Armor Digivolution, only accessible to certain Digimon from ancient bloodlines. This Digivolution was immune to the Digivolution cancellation effects of the Emperor's Control Spires

Six Digimentals were carried by the three DigiDestined empowered in 2002:

The Digimentals of Courage and Friendship were carried by Daisuke "Awesome Davis" Motomiya
The Digimentals of Love and Sincerity were carried by Miyako "Yolei" Inoue
The Digimentals of Knowledge and Reliability were carried by Iori Hida

The other two were carried by the two DigiDestined who had used the corresponding Crests in 1999:
The Digimental of Hope was carried by Takeru Takaishi
The Digimental of Light was carried by Kari Kamiya

All returned to their hiding places after the defeat of MaloMyotismon. Rumors of an unvieled ninth Digimental, the Digimental of Kindness, were never confirmed.

In Japan, there is also a Digimental of Darkness, but it has never appeared in any American material

Golden Digimentals
The Golden Digimentals are similar in some ways to the eight "regular" Digimentals, in that they are linked to the primal sigils and power Armor Digivolution, but are more powerful, creating Armor Digimon who's powers are more analagous to Ultimates. They are also more ephemeral, and when their task is done, they fade away until they are needed again.

The Golden Digimental of Miracles was used twice by Davis Motomiya; the first time, it was hiding with the Crest of Kindness in the reactor of the Digimon Emperor's fortress. The second, it was summoned by Magnadramon, the Holy Dragon of Light.

The Golden Digimental of Destiny was used once by Willis Gladstone. It was summoned by Seraphimon, the Celestial of Hope.

In Japan, the Digimental of Destiny was known as Fate

Spirits
(The Spirits are not canon in the Digimon Quest continuity)

The Spirits carry the power of the deceased Ancient Digimon, the ones who defeated the fallen angel Lucemon aeons past, and are based on classic Greek and Chinese elemental concepts. There are two Spirits for each element, a Human Spirit, and a Beast Spirit. A Digimon--or a human using a D-Tector Digivice--can access the power of the Spirits in Spirit Evolution, assuming the form of a Digimon. These Digimon do not follow the usual levels of Digivolution, and are referred to as Hybrids.

Fire Sprits

Source: AncientGreymon
Guarded by Seraphimon
Used by Takuya Kanbara
H-Hybrid: Agnimon
B-Hybrid: BurningGreymon
Fusion Hybrid: Aldamon

Light Spirits

Source: AncientGarurumon
Guarded by Seraphimon
Used by Koji Minamoto
H-Hybrid: Lobomon
B-Hybrid: KendoGarurumon
Fusion Hybrid: Beowulfmon

Thunder Spirits

Source: AncientBeetlemon
Guarded by Ophanimon
Used by JP Shibuyama
H-Hybrid: Beetlemon
B-Hybrid: MetalKabuterimon
Fusion Hybrid (theoretical): RhinoKabuterimon

Wind Spirits

Source: AncientKazemon
Guarded by Ophanimon
Used by Izumi "Zoe" Orimoto
H-Hybrid: Kazemon
B-Hybrid: Zephyrmon
Fusion Hybrid (theoretical): JetSylphimon

Ice Spirits

Source: AncientMegatheriummon
Guarded by Ophanimon
Used by Tommy Himi
H-Hybrid: Kumamon
B-Hybrid: Korikakkumon
Fusion Hybrid (theoretical): Daipenmon

Darkness Spirits

Source: AncientSphinxmon
Guarded by Cherubimon
Used by Koichi Kimura
H-Hybrid: (corrupt) Duskmon (true) Loweemon
B-Hybrid: (corrupt) Velgrmon (true) KaiserLeomon
Fusion Hybrid (theoretical): Reichmon

Metal Spirits

Source: AncientWisemon
Guarded by Cherubimon
Aided in the creation of MagnaGarurumon and Susanoomon
H-Hybrid: Mercurymon
B-Hybrid: Sephirothmon
Fusion Hybrid unknown

Earth Spirits

Source: AncientVolcanomon
Guarded by Cherubimon
Aided in the creation of MagnaGarurumon and Susanoomon
H-Hybrid: Grumblemon
B-Hybrid: Gigasmon
Fusion Hybrid unknown

Wood Spirits

Source: AncientTrojamon
Guarded by Cherubimon
Aided in the creation of EmperorGreymon and Susanoomon
H-Hybrid: Arbormon
B-Hybrid: Petaldramon
Fusion Hybrid unknown

Water Spirits

Source: AncientMermaidmon
Guarded by Cherubimon
Aided in the creation of EmperorGreymon and Susanoomon
H-Hybrid: Ranamon
B-Hybrid: Calamaramon
Fusion Hybrid unknown

Takuya and Koji's D-Tectors would later be upgraded to allow them to assume the form of Unity Hybrids. Takuya would fuse the spirits of Fire, Wind, Ice, Water, and Wood to become EmperorGreymon. Koji would fuse the spirits of Light, Darkness, Thunder, Earth, and Metal to become MagnaGarurumon.

All ten sets of Spirits used at once, which occured during the battle with Lucemon, create the Mega Digimon Susanoomon.

Digi-Soul
(Not canon in the Digimon Quest continuity)
**Data Squad Spoiler Warning**

Not technically Sigil artifacts, this is an ability posessed by some Tamers in Digimon Data Squad to trigger Digivolution by calling on their own emotional states. Masaru Daimon, for example, charges his Digi-Soul by punching his enemies; there is some verisimilitude between the Digi-Soul and the powers of Tai's DigiDestined to manifest their Crest powers even after the physical Crests were destroyed by Apocalymon. It probably works on some of the same metaphysics, but manifested differently

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