* Graduate: This refers to someone who has successfully completed a first degree (a bachelor's degree, typically a BA, BSc, or BEng). They are *graduates* of their university.
* Postgraduate: This refers to studies undertaken *after* a first degree. Postgraduate study includes master's degrees (MA, MSc, MEng), doctoral degrees (PhD, etc.), and other postgraduate qualifications like postgraduate certificates or diplomas. Someone undertaking postgraduate study is a *postgraduate student*.
Essentially, "graduate" describes the status of someone who has completed an undergraduate degree, while "postgraduate" describes the level of study *following* an undergraduate degree. All postgraduate students are graduates, but not all graduates are postgraduate students.