What is the actual meaning of a graduate program? Is it Masters? Or Ph.D. or Both? Does the definition vary from country to country?
It means both. It just means any programme that requires an undergraduate degree (such as a Bachelors: BSc, BA etc.) to enter.
It can be a taught course or a research programme, as there are both taught and research masters degrees. One has to look at the programme details to discover more.
I believe the definition does not vary from country to country as it just relates to the semantics of the English word.