Torah613Torah: I know plenty of people who think all Jews are either Satmar or not religious. Most of them live in either Kiryas Joel or Williamsburg.
As for differences between groups of Jews, I think that Modern Orthodox has the closest to the way Judaism has been practiced for thousands of years. Chassidus is a relatively new invention. The Besht felt that the common Jew needed a different way to serve Hashem, and so he created chassidus. It was not our mesorah to do things that way, the Besht just felt it was either that or lose all the common people.
The yeshivish mentality as it exists today is also a new derech. The Chazon Ish said after the Holocaust that people should be pushed to sit and learn in kollel, in order to try and replace the Rabbonim who were killed by the Nazis yemach sh’mom. He said this should be for 3 generations. Again, it was a new thing, not our mesorah, and was done because he felt the times needed it.
Modern Orthodoxy is called Modern because it deals with how halacha applies in the modern world – where the Shulchan Aruch and Mishna Brurah don’t tell us what to do, because the circumstances didn’t exist yet at those times. Jews going out to work and learning in the evenings, or going to a gemara (daf yomi?) shiur early in the morning, is how it was done for centuries.