Final answer:
The two main types of referendums in systems of direct democracy are legislative referendums, referred by the legislature, and popular referendums initiated by citizens. The terms 'Direct and Indirect' best describe these types, although these terms were not expressly used in the provided information.
Step-by-step explanation:
The two types of referendums described cover different aspects of direct democracy within the context of governmental structures, primarily in the United States. A legislative referendum occurs when a legislature refers a piece of legislation to the voters for approval or disapproval. On the other hand, a popular referendum refers to when citizens take the initiative to petition a disagreement with a legislature-enacted law to a public vote to potentially repeal that law.
Neither online nor offline, national nor local, mandatory nor voluntary specifically encapsulate the essence of legislative and popular referendums. The best option that fits the description of the types of referendums mentioned is Direct and Indirect, though these terms are not explicitly used in the provided information. This underscores the interactive process of both legislative bodies and the citizenry in shaping law.