Generally speaking, biomedical engineering is used to develop products, generally called medical devices, that aid in medical treatment (e.g. stents, bio-compatible materials, surgical implants and tools, prosthetics). Technical work will include designing and testing new products and/or developing new materials.
Generally speaking, the pharmaceutical industry is interested in chemical products (including protein and gene therapies) that aid in medical treatment, which include the pills, emulsions, ointments, and injectable solutions that doctors prescribe and use. Over the counter drugs are also part of the pharmaceutical industry. The technical work over the entire pharmaceutical industry is huge; the pharma industry employs microbiologists, pretty much every type of engineer, chemists, biochemists, statisticians, doctors, and other technical professionals that I can't remember at the moment.
Generally speaking, medical research is concerned with identifying the underlying processes that explain how the body works, how diseases affect the body, and how drugs and treatments affect the body. There is overlap with medical devices when the devices have to reside within the body, aim to replace a bodily function (e.g. machine to nerve connections). Medical research is the most different because it can be done entirely for the purpose of gaining new knowledge, there doesn't HAVE to be some product to be sold at the end of a project. Technical work for medical research will likely be lab oriented working with samples of bodily material, germs, and viruses (unless you go into medical research that is more based on studying human health behaviors, that a lot of data gathering/analysis).
Pharmaceutical companies may run or buy medical device companies because both of these product lines have to exist in a similar regulatory environment, so experience in navigating the regulations is a key attribute a larger pharma company could use to make a medical device company profitable. Furthermore, a pharmaceutical company will need medical research to prove a new drug class is safe and effective, so there is another way these fields relate.
**I have a feeling I'm not getting at the root of your question, so if you were looking for different kinds of information, please continue asking questions in the comments.