I'm pretty sure that Universal Suffrage would pertain to just that- universal suffrage, i.e. the system in most Western nations today. Sure, a multitude of referendums can be an extension of that, but the base meaning is just that everyone gets a vote- which is the case in the USA, and most other systems.
Take as evidence the respective messages 'We Love the Prime Minister Day' and 'We Love the President Day'. The first is indicative of some sort of higher executive power in government, whilst the second is indicative of the direct election of the executive power. Now, you can have a President without US and a Prime Minister with US, but the historical implications of such terms lend themselves to the qualifications I described previously.