In AE, graduate students (= grad students) are any students at a level above undergraduate. They have completed their bachelor's degree, but they may be master's or PhD students, or law, medical, or business school (MBA) students.
In some academic fields, if a master's degree doesn't bring much more in the job market than an undergraduate degree, these departments may not encourage or even offer terminal master's degree programs. So in these departments, the majority of grad students are in practice often doctoral students, but that's not the definition.
AE and BE uses of 'postgraduate' are also different. In AE it normally means 'postdoctoral' (= further research or study after having received a PhD), but in BE it can mean the group that in AE are called graduate students.
I can't say for sure what 'chapter' means in your example, but usually it means a local branch of a club or society. My guess would be that if there are enough students at your university to join as a group, they can all join for that rate, and they maybe only get one copy of the journal or whatever for the department instead of one per person, but they're all eligible to attend conferences and submit papers. But again, that's just a guess. You could certainly e-mail and ask.