One huge difference is in the narrator. In "The Celebrated Jumping Frog of Calaveras County," we have a first-person narrator, but it is really a 2nd-hand 1st-person narrator, one or two people removed. It is a very strange set-up. Twain, who is telling the story, is actually telling it in the words of other people. So, it isn't a direct tale, more of a legend or tall-tale sort of telling. Huck Finn on the other hand, is told in the first-person perspective from just one kid's perspective; there is no second-hand or third-hand passing down of lore. So, the narrators are different in that sense.
Other differences are a bit simpler and more obvious; one is a short story, one is an entire novel. One centers around just one guy and his propensity for gambling, and the other centers around the endearing friendship between a boy and a runaway slave. Jumping Frog is more of a singular satire of one particular situation, whereas Huck Finn is a huge collection of tiny stories and satires all stitched together as a quilt of the American experience. In Jumping Frog, the main character is a bit of a rascal, whereas in Huck Finn, the side characters are rascals. There is less of a moral point to Jumping Frog than there is in Huck Finn; Huck Finn is replete with little morals and lessons throughout.
I hope that those thoughts help to get you started; good luck!