What is the difference between Biomedical Engineering, Bioengineering and Biomedical Sciences?

These fields are being developed and structured right now, so there are no definite answers, specially in a world where interdisciplinarity is growing (and we can be grateful for that), so take the following answer with a grain of salt. Also, the examples are for illustration, can be incomplete/not the best. http://en.wikipedia.org/wiki/Biological_engineering is (opposing some previous answers) the broader term. It encompasses 1. Applications of different kinds of technology (electronic, mechanical, IT, systems engineering, ...) to biological problems. 1.a - All Mhttp://en.wikipedia.org/wiki/Biomedical_engineering#Medical_devicesechnology and devices and its implementation, http://en.wikipedia.org/wiki/Clinical_engineering 1.b - http://en.wikipedia.org/wiki/Bioinformatics, as in using old algorithms to deal with biological data 1.c - Technology for bio-research - using/developing technology to analyse/deal with biological samples - microscopes, incubators, sterilization equipment http://ofhttp://www.appropedia.org/Biolab_Equipment ) 1.d - http://en.wikipedia.org/wiki/Bioprocess_engineering and http://en.wikipedia.org/wiki/Bioreactor design ... 2 . The opposite, i.e. the application/inspiration in biological strategies to solve any problems.  2.a - http://en.wikipedia.org/wiki/Biomimetics (inspiration in biological systems to design any kind of technological solution) 2.b - http://en.wikipedia.org/wiki/Genetic_engineering -  finding natural living organisms and further engineering their natural capacities to produce things we need - bacteria to produce insulin, modified algae to produce food/biodiesel, modified plants to produce anything in large scale. The industrial implementation will require 1.d 2.c - http://en.wikipedia.org/wiki/Biopharmaceuticals, which can be seen as a subset of the previous. (the process of finding and getting ready for use any natural chemical mechanism of plants/bacteria/fungi to defend themselves for our own defense, or any other interesting product manufactured from them with medical application). . . . 3. Both - Any case where you have to come from the technology side (1) AND the Biology side (2) to solve your problem. That is the special case of http://en.wikipedia.org/wiki/Biomedical_engineering, where what matters is that the problem to solve is human health, but both approaches are taken (e.g. Medical devices (1.a) and Biopharmaceuticals (2.c) ) - any sub-field of the like,e.g.  http://en.wikipedia.org/wiki/Tissue_engineering - using materials science for the application in tissue regeneration or using the biological mechanistic of regeneration in humans (e.g. embryonic stem cells) or in other animals with more interesting regeneration abilities (sea stars, geckos...). . . . Bioengineering is many times taken as analogous to Biological Engineering, and semantically this makes sense (Biology + Engineering) and wikipedia takes them as synonyms. However in practice (Academia and Industry), Biological engineering is often related with industrial bio-production (as in Bioprocess Engineering and Bioreactor design) and Bioengineering to Biomedical engineering. Go figure out why. More philosophically, when we talk about any bio-related engineering, these fields are being developed right now, as the complexity of the cell and the biological systems is very large, as the application of mathematics (essential in any engineering) and certainty is harder and slower due to the many variables in the game. However, IT has been helping a lot with managing many variables (Big data, Genomics, Systems Biology...) +Engineering can take up assumptions with which you can ignore some degree of certainty with the help of the growing bio-sciences. Any (biological, biomedical, biomolecular) science is paving up the ground (hopefully more and more quantitatively) where the engineering will work and build on. I'm assuming you're asking about undergraduate programs. Specifically in the http://en.wikipedia.org/wiki/Biomedical_sciences that you asked, you should learn what are the kinds of human cells, tissues, systems; which are the human pathogens, virus, and the science of disease; and the sciences behind electronics, optics, and computers that could be used in the projects where a specific device/application will be designed, but this can vary a lot with the school. As a practical advice, if you're searching for real applied work/studies, choose engineering programs, and search throughout their courses/teachers and relation with industry and patent outputs. Choose biomedical sciences if you'd like to learn fundamentals that can later have applications, but if the design of those is not your concern. A serious discovery in biomedical sciences can sometimes have more impact on later, several fundamental and applied work, than a specific engineering attempt at one application. One good example (over 10000citations) http://www.sciencedirect.com/science/article/pii/S0092867406009767. However, if you want to be a real scientist, many times the undergraduate engineering programs will give you more tools and a a distinctive CV to learn and work in PhD programs. All in all, work hard and play hard. Good luck :)

In follow-up to Ming's answer, with which I agree, the tendency to interchange these terms is just as common in industry, especially since the use of the terms is much less driven by strict consideration of word or phrase etymology than it is by the scientific or technical credibility that manufacturers hope to garner by using these terms to describe their areas of expertise.

Right now frankly, not very much.  These names are pretty much used interchangeably in academia at the moment.  You should probably check the actual fields of research that your particular department of interest is doing to see if it fits well with you.