I live in Australia, and here we don't have cheese pizza... is it just an American name for a margherita or is it different?
Well, like all things pizza, it's ... complicated. At least here in 'Merica.
In the U.S., the term "Margherita" in reference to pizza is generally reserved for either the strictly Neapolitan-style pizza Margherita (above) or a sort of hybrid slice you'll often find in NYC by-the-slice pizzerias (more on that later).
A Neapolitan Margherita has a minimally doctored sauce of crushed fresh or canned San Marzano-style tomatoes (often only seasoned with salt) and is topped simply with mozzarella di bufala or fior di latte, basil, maybe a splash of olive oil and some salt. And, of course, it's almost always cooked in a wood-fired oven at high temperatures and for a very short amount of time.
This differs greatly from a "cheese pizza," which the majority of folks in the U.S. would recognize as this:
In NYC, though, we don't usually call it "cheese pizza," since a regular New York-style pizza is assumed to include cheese, making "cheese pizza" redundant. We call it a "plain pizza" or a "plain pie" and it looks like this:
There IS, however, a sort of hybrid pizza called a Margherita that you'll find in a typical NYC by-the-slice pizzeria. It's essentially the same New York-style dough, stretched to New York-style proportions and cooked in a standard gas-fired oven, but it's topped with fresh mozzarella, basil, and sometimes a different sauce than the pizzeria's standard cooked, heavily seasoned sauce. It looks like this:
Another note: I think it's safe to say that most people in the U.S., outside the Northeast and apart from Neapolitan-style junkies, typically order toppings on their pizza. Maybe this is just a cultural bias on my part. I grew up in the middle of the U.S., and people there looked at you weird if you wanted a "cheese pizza." In general we 'Mericans are large and in charge and like LOTS OF STUFF on our pizza: