Fossil horseshoe crab from Mazon Creek, Illinois. Not a dinosaur.
Roy Plotnick has an insightful blog post over on Medium. He discusses perceptions of paleontologists and Paleontology in general - who they are, what they do, and why it's important. Check it out! If you've read any of his previous posts, you'll know it's a great read!
The confusion with archaeologists is of somewhat understandable; scientists of both fields can spend a lot of time outdoors digging old stuff up from the ground. There are also strong overlaps in methods and concepts. Archaeologists and paleontologists are interested in dating what they have uncovered (although we rarely use carbon dating), in reconstructing the environment they formed in, and in the processes of biological decay. The theory of evolution underlies the two fields. Both sciences would also disavow Indiana Jones, who was not a paleontologist and was a very bad archaeologist (theft of cultural heritage, anyone?). Scientists from both disciplines also often collaborate. But at core, archaeologists are interested in the history of humanity, which is outside the scope of paleontological research.
Some paleontologists do indeed study dinosaurs. But most don’t. Dinosaurs, as wonderful as they are, are only a tiny fraction of the life that has lived on Earth and have been preserved as fossils. In truth, the majority of us study other parts of the huge tree of life and its history, which mainly occurred well before the first sauropod or theropod appeared.