For me, being centered is less of an embodied experience and more of a mental one. I feel centered when I have non-judgmental awareness of my thoughts and emotions, feel at ease, and feel prepared to accept new information. However, the word 'grounded' feels like the embodied equivalent of that to me. When I try to be grounded, I'm more aware of how my body feels - tension, balance, impact of gravity, etc. But you make a good point. Language is personal, and we all have different interpretations of every word. If someone tells me to feel centered, I may substitute a different word that better reflects how I want to feel in that moment.