Neither really. At least not for everyone.
Similar to trans it's just an additional information to someone's gender - a modifier, if you will. But just like trans some people do consider it part of their gender identity. For example: for some trans people their gender is simply female or male and the trans part is an obstacle to them. For others the struggle with dysphoria and the personal history of being misgendered and born with the wrong body influences their identity so much it becomes part of their gender identity - i.e. they're not just a woman but they're a _trans_ woman, meaning they are indeed a woman but their history of being in the wrong body is still part of their life.
Similarly, a genderfluid person might simply be fluctuating between two or more genders and consider these their gender identities (as in, there are multiple identities) and the genderfluid just described the fact they have multiple gender identities from time to time. Others might consider genderfluid to be part of their one gender identity or the "unifying connector" holding their different gender expressions together.
So, it can be part of a gender identity but it is not in and of itself a gender identity, let alone a gender. Look at it this way: Can you be just genderfluid? Without specifying what genders you fluctuate between? I don't think so. Just like you can't just be trans. Of course, there are genderfluid people who might not know what genders they fluctuate between or simply don't define each of the genders they fluctuate between because it would be difficult to describe or just take too long so they might consider genderfluid to be the "main ingredient" in their gender identity. But the actual genders are still in there somehow even if you don't quite know what they are.
Caption this Meme
