Final answer:
The referendum gives voters the ability to affirm or reject legislation already passed by the state legislature, providing a decisive method to overturn government decisions, while the initiative allows citizens to propose new legislation directly.
Step-by-step explanation:
The referendum and the initiative are both forms of direct democracy that serve to increase citizens' involvement in the political process. However, they differ in function and the degree of political power they grant to voters. A referendum allows voters to either affirm or reject legislation already passed by their state legislature, which can be seen as voters having the final say on laws that may have been influenced by special interests within the legislature. In comparison, an initiative permits voters to propose new legislation onto the ballot to be voted on, without it first going through the legislative body. This direct petitioning via initiatives can bypass potential legislative bottlenecks or special interest influence. However, referendums give voters the unique power to directly veto laws that have already been navigated through the legislative process, arguably providing a more immediate and decisive reversal of government decisions if voters disagree with actions taken by their elected officials.