In lieu of a list of traits that any species can have, most Lythian species and some companion species have something unique to each of them called subspecies, which are generally modified variants of the regular subspecies. They are typically less common than the basic individual and have their own lore under the "Subspecies" button on their species pages. They also tend to have slightly different appearances but are still recognizable as that species. For example, if you go to the Symphony page, you will find that the average Symphony is called a Natural, but there are a couple subspecies available to them.
Some subspecies can be created with just an MYO ticket, while others require an additional subspecies item. For example, if you visit the Axomaur page, you can see that they come in two subspecies, Aquatic and Terrestrial. Then, under the "Design Guidelines" button, there are bullet points for general guidelines that all Axomaurs have, as well as points for each subspecies. If the subspecies are marked with an asterisk (*), it means they require subspecies items to make (see Symphonies > Design Guidelines); if they are not marked, you can make it with just an MYO ticket (see Axomaurs > Design Guidelines).
The subspecies item required to obtain said subspecies is unique to each, as are the ways to obtain them. Some of them can be found in a shop after you've unlocked the realm that it's located in. Others may be seasonal and only return during certain events. You can also always check user shops
to see if anyone has any for sale!
After you obtain a subspecies item, you can apply it onto a new MYO Lythian when you submit them for approval. Or, you can use it on an already-existing Lythian to transform them and update their design.