Hey

Biomedical Science, Biomedicine, Medical Biosciences etc will teach similar content. So, if you're interested in Biomedical Science it's worth looking into degree's that have a variation of that title too (Medical Biosciences).
Module content will vary depending on which university you attend. So, there's not a distinctive difference between Biomedical Science and Medical Bioscience. Ultimately, you should treat courses such as Medical Biosciences the same as Biomedical Science but make sure that you view the module content before applying.
On a side note, have you thought about your profession after graduation? Do not worry if you have not. I mention this because of IBMS accreditation - something I think everyone should be aware of before applying to Biomedical Science. One of the most obvious jobs to apply for after graduation is "Biomedical Scientist", right? Well, you actually can't become one unless your degree has IBMS accreditation
This is why some universities might have two similar-sounding degree's such as Biomedical Science and Biomedicine because one will have the accreditation and the other won't. The non-accredited degree will, however, provide more flexibility when it comes to picking your modules so you can tailor your degree better.
With that said, there are so many options once you graduate with a degree in Biomedical Science because it's such a broad degree. So, if you want to work in any other bio-related job then it's not a concern. But, if you want to be a Biomedical Scientist you must check for IBMS accreditation before applying. Personally, I'm not sure what I want to do after graduation yet so I chose to keep my options open and picked a degree with IBMS accreditation just in case. To put it simply, in order to work as a Biomedical Scientist you need to be approved and this requires you to have studied a specific set of modules at university. You can still become a Biomedical Scientist if you have not got IBMS accreditation with your degree but it will require you to take top-up modules which are expensive and difficult to apply for.
Here is a list of all universities with IBMS accreditation
https://www.ibms.org/accredited-degrees/accredited-degree-courses/undergraduate-uk-courses/