How would one explain the distinctions between datim, chasidim, and charedim, especially to an American Jew who didn't know much about the Israeli religious spectrum? In particular, are all chasidim charedi?
Datim is generally the equivalent of Modern Orthodox in the US.
Charedim is an umbrella name for Chasidim, Yeshivish and any other variety of strict Orthodox who try to observe Jewish Laws and customs (e.g. the Shulchan Aruch and early commentaries) to the letter.
Chasidim are in the Chareidi category with an emphasis on minhagim which are largely based on Kaballah (even when sometimes infringing halachah). Additionally, Chasidim try to maintain a uniqueness and separation of the contemporary street a.k.a. Hisbadlus, and avoid exposure to non-Jewish values and ideas, like sports, TV and other hobbies which are otherwise permissible but have cultural implications and may lead one to be less connected to G-d and may hinder religious observance. This has been a major factor in the relatively low drop-out levels from chasidism compared to other groups.
While there might be some differences in customs and halachic positions, all of these groups believe in following the Shulchan Aruch. I would say that the biggest difference between Dati and Chareidi is that Dati men will generally get jobs to support their families and will join the army. Chareidim, including Chassidim, usually emphasize the importance of full time kollel torah study over everything else for men, and if men need to work for financial reasons this is looked down on, and joining the army is viewed as if you are abandoning the Torah.
Chassidim as a subset of Chareidim are followers of the Baal Shem Tov and his disciples.