In the USA we call them graduate students but they are doing post-graduate work. Graduate and post-graduate basically mean the same thing. The opposite is "undergraduates." Those students do not yet have their first 4-year college degree,

In the US systems, students at a college or university who studying for their degree (most commonly for a BA or a BS) are called undergraduates. Students studying for a Masters or PhD are called graduate students. Students studying for a medical degree (MD) are called medical students and must already have a BA or BS. But, the four years of medical school is considered undergraduate medical education while graduate medical education occurs during medical residencies and fellowships. Complicated, isn't it?

Graduate students, also called just 'grad' students, are studying for their Masters degree. Post-graduate students are studying for their PhD or doctorate.

That's a very good question! It really depends where you are, and who you ask. Technically, a "postgraduate student" is one who has a Bachelor's degree and is studying a non-degree programme, like a certificate or diploma (not a Masters or PhD). A graduate student is one who is enrolled in a Masters or PhD programme. However, the terms are used very interchangeably these days. "Postgraduate student" is more common in BrEng and "Graduate student" is more common in AmEng. We can also say "grad" and "postgrad", but those terms are quite informal.

Graduate Students