Undergraduate, graduate or post-graduate student — is that Bachelor/Master/PhD or Bachelor/Master+PhD/postdoc?
I am almost certain that post doc is not what is meant.
In English speaking systems outside of North America, and especially referring to Europe under the Bologna accords, an undergraduate refers to someone who is studying for, but has yet to receive, his first post-secondary education degree. Typically this degree is some equivalent of Bachelors, but in some cases students maybe enrolled in accelerated programs with a longer term of study that leads directly to (the equivalent of) a Masters degree.
A graduate student can, but not necessarily, refer to someone who is studying for a graduate diploma. In many countries having a Bachelors (or equivalent) is not sufficient in itself to qualify one for starting a postgraduate degree. One often requires a "good enough" Bachelors degree (such as one with honors). The graduate diploma is an intermediate step in which a student who has already received his first post-secondary degree studies further in order to qualify to enroll in a masters (or sometimes doctorate? I am not sure about this) degree program.
A postgraduate student refers to someone who has already obtained a first degree, and is now pursuing a second, third, or Nth degree beyond it. See, e.g. this Wikipedia entry.
A postdoctoral researcher is generally not considered as a student.
In English speaking North America, an undergraduate typically refers to someone studying for a bachelors, since almost all (if not all) degree programs go through that stage in North America. And a graduate student refers to any student studying for any degree beyond that of the bachelors (so that would be typically the masters or the doctorate).