Fellowships are usually for individuals and are designed to cover 100% of your time - both research and teaching - with the money you receive mainly being used to replace your teaching duties. This is designed to allow you enough time to complete a significant research project and will often be for a shorter duration than research grants. If your research doesn't require a big team or expensive equipment, but does require that you have some time to dedicate to pursuing it, this might be the form of funding for you.