(I have to admit I don't fully understand the difference between a two state solution and a separate country but I assume they want the West Bank and Gaza to be within the same borders somehow)
Let me try and help:
Two-State Solution - This is the most widely, mainstream, endorsed solution, especially by the so-called "international community", including the United Nations, the United States, and the European Union. It proposes the creation of an independent Palestinian state alongside the State of Israel. It has some variations to it, though:
- Mainstream Version: Envisions Israel and Palestine as sovereign, independent states, usually with borders based on pre-1967 lines, potentially with agreed land swaps and a shared or divided Jerusalem.
- Variations: Some proposals suggest different border adjustments or security arrangements. Specifically, some pro-Israel proponents envisage a version that sees Israel retaining overall control over the outside borders of the eventual state of Palestine. This is, generally speaking, rejected by Palestinians and their supporters as a version of "occupation light" as opposed to full sovereignty. Other proposals envisage a de-militarised Palestinian state - again, this is endorsed by some on the pro-Israel side and tends to be viewed with scepticism among Palestinians and their supporters - their primary argument being that nothing would stop Israel from invading and maintaining a de facto occupation / hegemony as it pleases in the absence of some sort of a "checks and balances" mechanism.
One-State Solution - This suggests that Israel and the Palestinian territories should form a single, bi-national state. Opinions vary widely on how this would be structured. Again, there are various versions:
- Equal Rights Version: Advocates for a democratic state where all inhabitants (Israeli and Palestinian) have equal rights. This idea is favored mostly by leftists. Ideas around its practical implementation vary widely, ranging from a "one size fits all" approach to suggestions modelled more along the lines of existing, multi-ethnic states such as Switzerland (a federation with far-reaching devolution of power).
- Annexation by Israel: Some right-wing Israeli factions favor annexing the West Bank and Gaza and, typically, offering limited rights but not full citizenship, to Palestinians. This would arguably be considered illegal under international law and is widely considered discriminatory. It would, however, also, essentially, be the codified continuation of the status quo.
- A Single Palestinian State: Basically the same thing as the annexation scenario - except "the other way around". Comes with all the same issues as the former - rarely ever discussed because nobody thinks it could ever realistically happen.
... and, of course, any number of "pretty crazy stuff people come up with", all of which are pretty niche.
HTH.