There are many different kind of Jews. The funny looking ones and the normal looking ones. In order to understand the discrepancies between different kinds of Jews it is helpful to understand what Jewish people believe first. Note, what I am about to say was not researched, this is just something that I observe, so I may be wrong on a few things.
Judaism believes that there was a follower of God called Avraham (Abraham), he was a devout and holy person. He was the first person to recognize God and live in the ways of God. He had a son called Yitzhak (Issac). This son was influenced by the father also to be a devout person. Later Yitzhak had a son called Yakkov (Jacob) who continued the tradition. But these people were not Jewish people, there was no such thing as Jewish people, you can call them the Hebrew people, but the notion of a Jew did not exist back in those days. Yakkov himself had 13 sons, one of which was Yosef. The other sons grew jealous of Yosef and eventually sold him in slavery. Yosef was taken down to Egypt, but he grew in his reputation. To the point that he became of very high status, not as high as the Pharoah though. But he was among the most powerful men in Egypt. The family of Avraham (that is, the Hebrew people) moved down to Egpyt, after all Joseph was of high status there. Over the years the Hebrews populated to high numbers (from 70 people to several million) after several generations. The Egyptians developed a deep hatred and fear for them. So the new Pharoah (this is many years after Yosef died) decided to enslave the Hebrew people and make their lives bitter. But a leader arose among the Hebrews (he was also an Egyptian, but I am trying to keep this very brief and do not want to get into the details) called Moshe (Moses). Moshe became the leader for the Hebrew people and a prophet of God, he made the Pharoah let the Hebrew people out from slavery through bringing plagues onto the Egyptians. When the Hebrews left Egypt in freedom it was not so long until the Egyptians realized they need to go back after them and bring them back. Now the Hebrews have an Egyptian army chasing them. But God brought forth a miracle, the splitting of the Sea of Reeds. The sea split in half, Hebrews pass through, but by the time the Egyptians are in the middle, the miracle ends and the Egyptians are washed away. This way the Hebrews got away from Egypt and were now freed. Moshe took them to Mount Sinai and recieved the commandments from God. This was also when the Hebrew people had the Torah (that is the Bible, given by God to the Jewish people). God promised the Hebrews that he would make them into a nation. But because they were sinful God punished them to wander in the desert for fourty years. It was during this time Moshe taught the Hebrews about the commandments of God. The commandments consisted of the "oral law" and "written law". The written law was the written Godly commandments, as expressed in the Torah. The oral law was what Moshe taught to the Hebrews. I will stop it at here, because the full story of the Jewish religion, even in compressed form is too long to say.
The important part that I want to express is what the oral law and what the written law is. Both of these laws come directly from God. Jewish people often do things not mentioned anywhere in the Torah. Why is that? This is because there is an oral commandment to follow. Take for example the yamalka. Nowhere in the Torah does it say to cover one's head. The oral law does talk about covering one's head. One also needs to understand that whereas the written law was always available in a book, the Torah, the oral law had to be passed down from generation to generation. The current Rabbis taught the current students and the students later became Rabbis themselves to teach it down to the next generation. The interpretation of the Torah (the written law) is heavily based on the proper understanding of the oral tradition of the Rabbis. This is why it is the Rabbis themselves who can interpret the commandments of the Torah because they know the oral tradition. This is what the Gemara (Talmud) is about. It is a collection of many oral traditions and how it applies to the interpretation of the Torah.
With the above background we can explain the various types of Jews.
Orthodox: This is the oldest form of Judaism. The Orthodox Jews believe in exactly what is written above. They believe it is their mission in life to follow the words of the Torah and Rabbis. Orthodox Jews also try to stay away from the outside world. They may not own any TV's. They do not listen to non-Jewish music. They do not read non-Jewish magazines. They do associate in the modern world. They can have jobs as professors or lawyers or doctors. But their identification of the modern world is limited. They often wear black suits and black hats.
Ultra-Orthodox: In case the Orthodox are not crazy enough we have another group of Jews that are even crazier. The Ultra-Orthodox Jews arose in the 1700's and 1800's. They were a reaction of the hashkalah (Jewish Enlightenment). They reacted by being more observant than they had to be. The Ultra-Orthodox Jews believe in exactly the same as the Orthodox, indeed they sometimes pray in eachother's synagogues. They differ in that the Ultra-Orthodox Jews completely seclude themselves from the outside world. Whereas, the Orthodox Jews can live in a non-Jewish area just fine, the Ultra-Orthodox make their own communities and isolate themselves entirely from the outside world. They often wear those funny looking huge fur hats, long white socks, and peious. They are also called hasidim (or Charedim).
Modern-Orthodox: The Modern-Orthodox Jews believe in what the Orthodox Jews believe as well, however they are more open to associating with the modern world. They are more liberal than the Orthodox. So they would not have a problem with going to a movie theater with a non-Jewish college classmate. These Jews dress in typical average day clothes. They may wear jeans or t-shits, nothing to formal like the Orthodox. Their yamalka is even more artistic, in contrast to the Orthodox yamalka which is a big black velvet one.
Reform: The Reform Jews actually go out of their way to reform the Torah and the lifestyle of Jewish people. This started during the hashkalah movement. Many of them do not even wear a yamalka. They (common Reform Jews, not talking about the Rabbis) are not very knowledge about as Judaism as much as the Orthodox are.
Conservative: Conservative Jews were a reaction to the Reform Jews. They saw the Reform Jews as going too far. For example, the Reform Jews actually reform the commandments of the Torah. Conservative Jews still consider the written law to be binding, for it comes from God. But they say that we need to reconsider the oral law and see how it applies to modern times. So they do not segregate men and women in synagogues because they say that is an outdated oral tradition which is not present in the Torah whatsoever.
Reconstructionist: These are basically Jewish people who realized the Torah was not written by God but by man and now they practice Judaism only as a ritual. They follow the commandments unless there is good reason not to practice them. So they may keep Shabbos to an extent or even kosher. Only because they want to hold on to the tradition and thing it is a good idea.
Humanistic: These are Jewish people that do not practive Judaism and do not believe in Judaism. They still enjoy being part of Judaism and its poeple. I think of myself as being a Humanistic Jew.
Secular: This is quite obvious. Jewish people that have nothing to do with Judaism anymore.
An easier way to classify Jewish people is from most-craziest to least-craziest, so the list would be: