Biomedical is anything relevant to human disease (Biology + Medicine).
"Basic" research refers to research of the kind that seeks to create new generalizable knowledge about the world, usually by elucidating the mechanisms or principles associated with empirical observations. Basic, in my mind, exists on the far end of a spectrum which starts with "theoretical" on one side and ends with "translational" or "engineering" on the other. Trying to understand the mechanism of inactivation for an ion channel in a particular type of neuron is basic research. While theoretical research can be grounded in empirical observation, it's goal is to generate new testable hypotheses (or testable some day in the future) or take a broad swath of observations and make their underlying principles immediately comprehensible through mathematics and logic. E.g. attempting to create a model capable of predicting protein secondary and tertiary structure from a DNA sequence can be considered theoretical work. Translational research, on the other hand, aims to take discoveries from the basic sciences and "translate" them to direct applications. In the biomedical sciences we call this "translation" but everywhere else it's called "engineering". I.e. basic research has given you new knowledge and now you try to "engineer" a solution to a known problem utilizing that knowledge. Engineering tissue chips capable of replicating tissue micro-environments without the need of an animal model is one "engineering" type example, but trying to develop a drug that inhibits a membrane transporter recently discovered to be responsible for some disease process is perhaps a more common instance of "translational" type research.
Clinical research is done on and with patients. It can be anything from designing an experiment in which you plan to measure some kind of response in live patients under some conditions or simply running some statistical analyses on compiled cohort data to try to tease out an association no one else has thought of looking for before.
Science is also synonymous with "the best".