As an example for the deck sorting:
https://deckstats.net/decks/140995/1415838-mayael-the-anima/de?revision=29If you sort by color, you will e.g. find
Boros Signet in the multicolor section instead of colorless.
Skyshroud Elf is also in the multicolor section but should be green. So the sorting is correct in terms of color identity but not color of the card.
The comprehensive rules say about color (excerpt):
202.2. An object is the color or colors of the mana symbols in its mana cost, regardless of the color of its frame.
202.2b Objects with no colored mana symbols in their mana costs are colorless.
Whereas color identity:
903.4. The Commander variant uses color identity to determine what cards can be in a deck with a certain commander. The color identity of a card is the color or colors of any mana symbols in that card’s mana cost or rules text, plus any colors defined by its characteristic-defining abilities (see rule 604.3) or color indicator (see rule 204).