A graduate degree is awarded after attending graduate school. A graduate degree is a masters degree, which generally takes 2-3 years of graduate school after college.
Undergraduate coursework is a basic educational foundation within a given program of study following high school. The course work includes a general cluster of knowledge that promotes a well rounded education. Thus, the student is exposed to a variety of areas, not just their chosen field of study. These areas would include general education courses to include, English, Math, History, Laboratory Science, courses in Humanities, and Social Sciences to mention a few. These would be tightly coupled with the students Major Requirements and Major Elective Requirements.
In the UK...
In the UK, the descriptors as to what constitutes an Undergraduate / Bachelors Degree and a Graduate (Master's or Doctoral) degree is set by the Quality Assurance Agency for Higher Education (QAA) in their document "The framework for higher education qualifications in England, Wales and Northern Ireland".
In it they specify that a Bachelors Degree is a level 6 course in the Framework for Higher Education Qualifications (FHEQ) system.
Any course above this level is a graduate degree or equivalent (e.g. Master's Degree or Postgraduate Certificates at level 7 or Doctoral Degree at level 8).
They also outline the differences between the two levels of qualification and the expected requirements and outcomes of having studied at the differing levels.
In the USA...
In the USA, information on the difference between varying levels of tertiary (post high school) education is given on the US Department of Education website.
In general the following applies:
In the US there are 6 main levels of post high school education:
1. Associate Degrees
2. Bachelors Degrees
3. First-Professional Degrees
4. Master's Degrees
5. Intermediate Graduate Qualifications
6. Research Doctorate Degrees
Level 1 and 2 count as undergraduate courses of study. Above this level the qualifications require an undergraduate degree or period of study as a prerequisite and so are termed graduate courses.
Both Level 3 and 6 qualifications commonly lead to the title of Doctor, however level 3 qualifications are professional doctorates such as those in medicine e.g. MD, whereas level 6 doctorates are research or academic doctorates e.g. PhD.
In general in the USA:
• Undergraduate courses involve study in Freshman-Senior courses with the aim of gaining a Bachelor's or Associates Degree.
• Graduate courses involve study for a higher level qualification which has an undergraduate degree as a pre requisite requirement.