Although I did not obtain a Biomedical Engineering PhD, I do no a couple of people that did. I was in a MRI lab at UTHSCSA. I see that you also live in San Antonio. The 2 people that I know that did obtain a Biomedical Engineering degree were in a dual program with UTSA and UTHSCSA. They both worked with me in the same lab. While I was more interested in using the MRI/MRI technology to better understand disease, both of my lab mates were interested in enhancing the technology of the MRI to help better understand disease. I would say that a biomedical engineer is more interested in answering questions about the technology while a scientist might be more interested in answering questions about a disease using that technology.
As far as I understand and know, they were taking classes about MRI, radiology, physics, medical physics, and molecular medicine. Therefore, as an undergrad, you may have to take more science and engineering classes that either alone.
My biggest advice is to really think where you want to go and what you want to do after grad school.
I hope some of this information is useful to you and if you like to know more, please do not hesitate to respond with more questions. I can always contact my two friends for more detailed answers.