Parts of this are headcanon supplementing explicit canon information.
In Tales of Symphonia, Exspheres are inorganic crystalline life forms some of the people of Aselia equip to draw out and boost their body's natural abilities. However, Exspheres are parasitic and grow stronger by feeding off of the suffering of their bearers; they require a Key Crest to allow them to be used without warping the user's mana, which if left unattended can distort a person's body and mind.
Under certain conditions, an Exsphere will evolve into an even more powerful form known as a Cruxis Crystal. Aside from boosting a person's latent abilities even further, Cruxis Crystals have one main other use: they can trigger the user's evolution into an angel. Angels have increased strength and senses greater even than an Exsphere user's, the ability to use a specific set of spells, and of course wings; they can also, if they so choose, manipulate their body's mana to stop their biological clock.
This transformation into an angel through the use of a Cruxis Crystal's parasitic infection is the goal of the Chosen of Mana's journey of world regeneration ritual. Upon receiving an oracle from Cruxis, the Chosen is equipped with a Cruxis Crystal with no Key Crest. He or she then journeys to and releases each of his or her world's four elemental seals, where Cruxis advances the angel transformation process a further step. In order, they lose their appetite and their ability to eat, their ability to and need for sleep, their ability to cry and to feel physical sensations (such as pain), their voice, and finally in the end the Cruxis Crystal consumes its bearer's soul, leaving the body a vacant vessel to be inhabited by the Goddess Martel. As Sylvarant's Chosen of Mana, this is what Colette endured to save her world, but it can be and was reversed by a Key Crest. Her lost senses and soul have been restored to her.
Although those who go through the angel transformation are identified as angels, they are fundamentally still whatever species/race they were born as. Thus, in Colette's case, she is still fundamentally human. I think this for a couple of reasons:
1.) Neither of the party's half-elves, who can perceive mana the way people can perceive color and temperature, remark on Colette's mana changing. Her mana signature itself remains completely unchanged by the Cruxis Crystal's parasitic infection. As the Chosen lines were bred specifically to create a vessel with a mana signature as close as possible or identical to Martel's, this suggests that a person's mana signature is biological and cannot be changed by the Cruxis Crystal's ability to warp its host's mana.
2.) In both his bad end and in the sequel game, Zelos has access to several high-level angel spells (most notably Judgment and his Mystic Arte, Shining Bind), which suggests he went through the angel transformation before joining the party, as Judgment is the last angel spell that Colette obtains. However, when with the party before his boss fight, Zelos shows no hint of angel abilities whatsoever. Of course, Zelos is a liar, but he's a liar who looks out for his own skin. In one notable scene both Colette and Presea hear the Papal Guard approaching, while Zelos clearly does not. He mentions that he received his Exsphere from the Renegades (likely the truth, since Sheena did as well and was present for the conversation), but before betraying the party, he retrieves his Cruxis Crystal from his sister and swaps out his Exsphere for that. Cue boss fight (depending on his ending), and Zelos suddenly has wings.
3.) The Cruxis Crystal's parasitic infection slowly spreads without a Key Crest, but with a Key Crest it is inhibited. So when a Key Crest is equipped, it prevents the Cruxis Crystal from completely overtaking a person's mind and body.
In other words, Colette is still human, but having her Cruxis Crystal equipped makes her an angel: without it, she would be a human. In RP terms, I think this would manifest for characters with special senses in two ways:
Spiritual senses (e.g., holy beings, other angels, priests/esses, etc.) can detect something holy about Colette, but the source is her Cruxis Crystal itself. It also wouldn't feel like a typical Biblical angel, because that's not what Cruxis Crystals or Symphonia angels are. They merely have access to holy magic.
Magical senses (e.g., mages, etc.) can detect magic in Colette, but not the same kind of magic a typical mage might have. Mages in Tales of Symphonia all have elven blood or are humans who have ingested a mana-suffused rock called aionis; Colette is not the first and has not done the second. She can use angel spells and only angel spells: no fire, no ice, no wind, no etc. In other words, she might feel slightly more magical than a regular human, but less magical than an actual mage.
Anyone who can sense life auras or anything of the sort will be able to detect that the innocuous red gem embedded in Colette's collarbone is very much alive and has a symbiotic relationship with Colette's life energy. It may also have some trace of the souls it has consumed in the past. Those souls are officially dead--they no longer inhabit the crystal, having been overtaken and devoured by it--but if souls leave any trace residue, it is detectable.
If you have any questions, let me know!