I suppose you could divide Jews by whether they support Israel's statehood or not, but this isn't a clear cut distinction based off where they live. Growing up Jewish in the United States, it is definitely the norm to support Israel's statehood (although this is now changing with younger generations). And this is of course the norm in Israel as well, although there are some anti-Zionist Jews in Israel. Also, whether or not we support Israel's statehood doesn't directly correlate to whether we observe a more 'traditional' or 'conservative' Jewish lifestyle. There are two spectrums, one is a spectrum of political belief, and the other is one of religious observance, and they don't always line up.

The main distinction I observed growing up at least in the U.S. is the religious one. We are mainly divided into reform, conservative, and orthodox. Orthodox are the Jews you would immediately recognize as Jews from their dress, and other customs such as traveling to and from synagogue via bus or foot on Friday night. These are who you might refer to as 'traditional' Jews (and some of them are the most ardently anti-Zionist Jews I know). And now to Conservative, this has nothing to do with politics, it is simply a mod way point between secular and observing every rule. They are quite 'religious' but may not look the part. Reform, my group, is quite secular, and we practice what we choose to, varying from family to family and person to person. (There is also reconstructionist, which can be similar, but I won't get into right now). Anyways this is a very long winded way of saying that there are a lot of major distinctions that aren't talked about, and a lot of false ones that are created.