It is really a combination of things. I'll post a few pics for clarification. All of these can be purchased through the Scottish Tartans Museum gift shop:
http://giftshop.scottishtartans.org/sporran.html

First, here is an example of a fairly typical "day" sporran:

All leather, no fur. Leather flap for a closure.

Now, here is an example of a fairly typical "evening" or formal sporran:

Fur body (in this case white), round metal cantle.

Is it the fur or the metal cantle that makes it formal? Well, here is a sporran with a round metal cantle, and a leather body:

I would class this as semi-formal. No, it's not as formal as the white fur one pictured above, but it is by no means casual. I would feel comfortable wearing this with a black Argyle jacket and long neck tie. I'd also say it would go well with a Prince Charlie and bow tie if one were looking for a non-fur sporran option.

Does it work as well the other way 'round? In other words, what about a fur sporran with a plain leather flap closure, like this one:
http://giftshop.scottishtartans.org/DSCF1130_038.jpg
I don't think this works as a formal sporran. Leaving aside the fact that the use of brown leather makes it more suited for casual, I think even if we imagined this style with white fur and black leather, it still would not be as formal as the non-fur, metal cantle variety pictured above.

So it would seem to be the metal cantle that is most key in defining a "formal" vs. "casual" sporran. But that's really not a cut and dry rule. What would you say to a sporran like this?

It's fur. And it has a leather cantle. But the cantle is a round one, in the same shape and style as the metal formal cantles; itis not a simple flap. I'd say this one would work perfectly well for formal wear, even black tie. But because of the lack of metal shinies ("bling") I think one could also get by with wearing it with a more dress-casual look.

And what about this:

Full mask sporrans can be worn either as formal or casual wear (again, when I say casual, I mean dress-casual day wear, not ultra-casual sandals and t-shirt mode).

And what about this:

This is the Duin uassal from the Ferguson Britt line, in black leather. I call this one the "only sporran you ever have to own." I say that not only because the construction on it will last a lifetime, but because I think this is equally suited to be both a very nice daywear sporran (because it has no fur, and no metal), but also a nice understated evening sporran (because of the style of the sporran cantle and body, the elegence of the look, the quality black leather, and quality construction). Perfect!

So what defines a formal sporran v. a casual sporran? It's a number of things in combination, really, and there are many styles of sporran that can readily be pressed into double duty if needs be. Thus concludes this photo essay!

~M