There are three main denominations in Judaism. Orthodox, Conservative, and Reform. Orthodox Judaism is very strict and Orthodox Jews attempt to follow all 613 commandments as best they can. Orthodox Judaism sees the Torah as the absolute law that must be followed. Conservative Judaism is somewhat less strict. Conservative Jews follow many old traditions but are not as forceful of the laws and embrace some new concepts. Reform Judaism sees the Torah as a moral guide more than a rule book. Reform Judaism is very relaxed.
Orthodox Jews abide by the commands of the Torah and the Oral Torah (Talmud).
Orthodox Jews learn the Torah as God's words and fulfill its laws.
"Progressive" implies change. Orthodox Jews are those who believe in God and the Torah, and keep the commands of the Torah (Sabbath, Kashruth, etc.).
Hasidim are a portion of Orthodox Jews. They follow Judaism on a strictly Orthodox level.
Orthodox believe that EVERYTHING should be done in accordance to the Torah at all times - NO exceptions.
Saturday is the Sabbath in Judaism. Orthodox (and some non-orthodox) Jews will not work. Many non-Orthodox Jews will work, but still remember the Sabbath day in their own ways. (And yes, there are some Orthodox Jews that work on Saturdays, but they do not advertise this fact).
Orthodox Jews follow strict tradition and Jewish law, whereas the Conservative movement has relaxed some of the observances.
Many Jews are termed "secular Jews", that is they identify as Jewish for cultural reasons but do not believe in God or Judaism.
Orthodox Jews, as well as other Jews, are able to do whatever they want to do. Those Jews ... Orthodox, Conservative, Reform, or any others ... who decide to observe and adhere to the formal standards and teachings of Judaism do not eat pork. In that respect, they are mirrored by Muslims and Hindus. Orthodox Jews, though, are more likely to observe and adhere to that standard than Liberal Jews (like Conservative, Reform, and Secular Jews).
Modern Orthodox Jews consider themselves bound by the 613 commandments in the Torah as understood by the unbroken rabbinical tradition from biblical times to the present. In this regard, they agree with Hassidic Jews. Modern Orthodoxy generally accepts the role of modern science and engages vigorously with the secular world. Where Hassidic Jews dress very distinctively and frequently minimize their contact with the secular community, modern Orthodox Jews are likely to blend into a crowd, with perhaps only a kippah (yarmulke) identifying them as Jews. Where Hassidic Jews view a yeshiva education as normal, Modern Orthodox Jews go to universities and graduate programs -- although significant numbers attend Yeshiva University, an Orthodox university.
There are many differences among American Jews and Israeli Jews. In the United States, the majority of Jews are Ashkenazi (though there are some Sephardic Jews). Also, American Jews often make specific distinctions between Reform, Conservative, Secular Humanist, Reconstructionist, and Orthodox, whereas in Israel, people tend to be secular Jews, reform, or Orthodox. In the U.S., Jews have to make an effort to celebrate the holidays or go to services, but in Israel the holidays are essentially automatically in the calendar, and Judaism is kind of all around. Some American Jews know few other Jews, but the majority of Israeli Jews know lots of other Jews.
Hasidic Jews are a subcategory of Orthodox Jews. The majority of Hassidim wear long coats, while most other Orthodox Jews wear regular suits. On Sabbath and festivals, Hassidim wear a fur hat called a streimel, while other Orthodox Jews wear hats more similar to standard styles.