It's confusing because it's complicated!
Israel is carved up into Israel as a country, and then increasingly fragmented land around it outside of Israel's borders, but not in another country. This is the Palestinian territories. West Bank and Gaza.
Keep in mind, Israel is a country with normal country stuff. Palestinian territory is NOT a country, and they are occupied by Israel, so Israel everything that goes in and out. Life in the territories is often intolerable and a lot of people are killed by Israel.
The current conflict is between Israel, and a Palestinian organization called Hamas.
And Hamas want to destroy Israel and get their land back. So Hamas have a history of attacking Israel in any way they can, frequently through acts of terrorism. This is in response to Israel causing a lot of death and destruction in the Palestinian territories but "who started it" doesn't matter at this point.
The current conflict is between Israel and Hamas.