Graduate certificates and diplomas generally fall into one of three types:
Graduate Diplomas: sometimes offered for students who have a degree but do not have the specific area of expertise to undertake a particular, usually very specialist, masters degree offered by the same institution.
Postgraduate Certificates: the most well-known of these is the PGCE, required for teaching in most schools in the UK. Students must generally have a first degree.
Postgraduate Diplomas: these tend to be either:
ThinkPostgrad: Postgraduate certificates and diplomas are often linked either to other qualifications and courses, or to a profession. It is useful to clarify these links, and whether the course you take needs to be accredited by a particular professional body, as well as whether other qualifications may be required subsequently, before applying for this type of course.
You can start looking now for masters course opportunities with funding on PostgraduateStudentships, or for masters courses in your subject area on MastersCompare.