Kupat Cholim was originally a Bolshevik Histadrut thing. Kupat Cholim Klalit was their health system. The other parties also set up health systems. In Israel everything is political which is why the other health systems and even sports leagues are named after political parties. Kupat Cholim Klalit doesn't exist anymore. It's called Sherutei Briut Klalit but people still call it Kupat Cholim Klalit. You used to have to be a member of the Histadrut labor union to have Kupat Cholim Klalit insurance. But the Knesset passed a universal healthcare law in the 1990's that says anyone can get health insurance. To get health insurance, you have to pay money to the National Insurance Institute (which is similar to Social Security) but I think people who are unemployed or get NII monthly payments get free health insurance. When I lived in Israel, I was a student so I had to pay the student rate. Probably the more someone makes, the more they have to pay. You also can't register as unemployed if you are a student.
Kupat Cholim is very bureaucratic. If a medicine isn't listed under the Health Ministry list of medicines, it cost a lot of money. If it is covered, then you pay per pill, not per prescription like in the US where if you have insurance, you pay a set co-pay. It can also take months until you can get an appointment to a specialist in Israel.