One can send chakra out of any part of their bodies, the other send their body out with their chakra.
I originally thought it would be something like,
The Hyuuga can release chakra , while the opposing part can store and control chakra.
The Hyuga can expel chakra out of any part of their bodies. Kaguya can send her body anywhere with chakra. I originally thought it was something like that.
The Hugs expel chakra. Kaguya stores and controls it.
^^^ that is what she's saying.
OT: Uh, really isn't some difficulty concept. Kaguya is simply the progenitor of the Hyuga. She is simply using the equivalent of ninjutsu to teleport. Mixing her Byakugan, Sharingan/Rinnegan, and ludicrous chakra levels to do so.
Consider it Kamui, but simply on a far better scale. There's no Hyuga-Kaguya "thing." It's just Kaguya being OP.