This is really funny - I've eaten gumbos and jambalayas and etoufees all my life (well, since I started eating solid food when we lived in New Orleans - along with boiled shrimp, crab and crawfish) and made them for 35 years or so - but never really thought about the differences. I just knew what they were - never tried to different what they were in terms.
I totally agree with Andy M. - filé is not a mandatory ingredient for gumbo.
The difference is that Jambalaya is a rice dish - probably a Creole adaptation of paella using locally available ingredients. Read Chef John Folse's comments
here. Supports most of what VeraBlue and Uncle Bob said about it's origin.
Gumbo - a thick savory soup or stew - usually starting with a roux (Jambalaya doesn't) for both thickening and flavor (the darker the roux the more flavor). I have run across a couple of recipes where the roux is added at the end .... but every gumbo recipe I have seen includes a roux somewhere. Reminds me of Justin Wilson's mantra ... "First you make a roux."
Now, I like Chef Paul, and I love eating at K-Paul's - but I hate that you have to buy his "magic" this or that seasoning to make anything following the recipes on his website. Maybe that is why I like his "Prudhomme Family Cookbook" the best?
Here are some recipe options
from Chef John D. Folse - another Cajun chef. Click on "soups" for gumbo recipes, click on "meats" for jambalaya recipes. Click on anything for delicious ideas. And, you don't have to buy any propritery spice blends to make them. And, they are more like what Uncle Glenn and Aunt Margaret used to make ... and Uncle Glenn is a back woods card carrying Coon-A ....
Laisez les bons temps rouler!