I've never seen a gumbo referred to as being either cajun or creole, but I have seen certain gumbos that are more commonly found in one cuisine than the other.
One main difference between the two--and there are many--is that cajun cuisine's roots are from the acadians of southern & now mainly southwestern Louisiana while creole cuisine comes from the mixture of french and african traditions and is better represented in the city of New Orleans.
Both can be found in either place, and as much as they are different, they are the same. It'd be like comparing Northern Italian and Sicilian cuisines: very different, but to an outsider, very similar.
There are no set rules differentiating the two's gumbos, though. There are some generalities that sometimes are more popular with one or the other. I've found that duck and andouille gumbo seems to be more popular with cajuns, and seafood gumbo seems to be the standard around new orleans. But, you can easily get a cup of seafood gumbo anywhere in Lafayette, and I'm sure you can find some good duck and andouille in New Orleans.
I've had some cajun people's gumbos that seem to be made with really dark rouxs like Paul Prudhomme, but then again you see these all over New Orleans. I've seen cajuns eating light sipping gumbos made with a blonde roux too. I've heard one cajun argue with another that seafood gumbo shouldn't have chicken or sausage in it while another said, "Throw it all in there."
I've seen people from Lafayette put potato salad in there gumbo--usually you see it with rice--and I've talked to some Louisiana natives that think that's the craziest thing they've ever heard.
Anyways, to answer your question, there are no rules on how exactly to make a gumbo--other than you start with a roux (there are plenty different styles of roux), and add the trinity of onions, celery, and bell pepper. Everyone makes them different. If you walked into a cajun restaurant and then a creole one, they would probably have very different gumbos, but then again, if you walked into ten different creole restaurants, you'd probably get ten different gumbos too.
Below are some very informative links on Wikipedia.