Could someone please explain to me the difference between a Type 1 Nova, and a Supernova?
Type I Novae are a subset of all supernovae. Roughly speaking, supernovae are classified by looking at the spectral lines in the light they emit when they are at their peak brightness. If there is evidence for hydrogen in the spectrum they are called "Type II", if not they are "Type I."
Within the Type I class they are further subdivided by what other elements are present. For example, if their is evidence for Silicon in the spectral pattern then the novae is classified as Type Ia, and so on.
The type Ia supernovae are special in that they are very well understood theoretically. They are believed to be the result of the explosion of a carbon-oxygen white dwarf star. The computer models that theorists have used to understand the duration of the explosion and the spectral lines are very good at reproducing the data for this class of novae. Since they are so accurate in these details, it is reasonable to assume that the models are also predicting the correct absolute intensity of the light as well.
That's important for the following reason. If you look up into the night sky you see a lot of stars. How do you tell which ones are far away and which are close by? You might think the bright ones must be closer than the dim ones, and that would be a good assumption if all stars were equally bright (say as bright as the sun). But of course, they're not equally bright.
But we believe all type Ia supernovae are equally bright, at least to a reasonable degree of accuracy. Hence the name "standard candles" to refer to these objects. So when we see a supernova with the characteristic spectrum of a type Ia nova then we can look at its apparent brightness to gauge its absolute distance. And this lets us study how certain cosmological features may change with time, since the more distant an object is the farther back in time when its light was emitted to reach us now.
There is some information about these novae and how they are used at the LBL website:
Brent Nelson, Ph.D., Postdoc, University of Pennsylvania