Hi there. I think in broad strokes, you've already received an answer that (while I quibble with the factual accuracy here) on some points, is good at explaining the differences largely. The Northern Cyprus situation was borne of ethnic divisions where a larger power (Turkey) intervened and occupied the area. There were disputes over how much independence Northern Cyprus actually had, given the Turkish occupation and presence of soldiers there. The Israeli-occupied territories are different. Israel took them over following a war with other existing states, rather than a civil war where there was intervention, and Northern Cyprus is far more happy with independence/occupation than the Palestinian territories ever were.

The "justness" of their actions depends on what you grade by, and that's not necessarily historical. I can't really grade it on a moral standpoint. From the standpoint of international law, Israel would have more ground to stand on for the way the occupation began, however. Turkey invaded an existing state without any reasonable claim to self-defense, while Israel took over the West Bank, Gaza, the Sinai, and the Golan Heights (some of which it later evacuated of course) during a war against Egypt, Jordan, and Syria. Its attack on Egypt is contentious, though the majority of scholars have concluded that it was justified, despite being pre-emptive. Pre-emptive strikes are one of the most contentious topics in international law in my opinion: they have an extraordinarily high bar for when they can be just. They require a whole host of criteria to be met under the criteria of jus ad bellum (based on the older Caroline test), such as attacking as a last resort (after all other options are tried) and with just cause (i.e. a legitimate reason).

However, the occupation of the West Bank and the Golan Heights, separate from Gaza and the Sinai, is less contentious in my opinion as far as the international law goes. Those territories were controlled by Jordan and Syria, which attacked Israel after it went to war with Egypt. Jordan in particular was asked to remain out of the war with promises that Israel would leave it alone, which would mean it didn't satisfy any "collective self-defense" strategy very easily, and certainly didn't meet the "last resort" standard since it had other options quite clearly. The occupation therefore began in more justified ways under the law.

However, one could argue Turkey was justified, because it was welcomed in by the Turkish population of Cyprus. Still, that argument is unconvincing as far as international law goes, because the existing sovereignty of a state usually can't be violated, even if it is fighting or in a civil war, not without legitimate reason. The law would usually dictate that Turkey had to get some kind of authorization from the UN Security Council, or find justification under some of the treaties governing justified use of force, none of which applied and some of which were not created at the time of the occupation. The closest justification would be, in my opinion, the "responsibility to protect" doctrine, but that wasn't formulated or even close to becoming customary law (and largely still isn't) at all.

There is one similarity I would draw however, and that's between the Turkish and the Arab occupations. When the 1948 war occurred, Jordan occupied the West Bank and East Jerusalem and Egypt occupied Gaza. While they were not really "welcomed" into the area, and never gave any measure of actual independence to those territories, they are the closest parallel in my opinion to the Turkish occupation of Northern Cyprus that you can find in the Arab-Israeli conflict. Friendly-to-the-Palestinians and larger nations intervened in a civil war (between Jews and Arabs in 1947), did not occupy the entire area (Israel was still founded), and did so on behalf of their friends. However, Northern Cyprus gained more independence and was not lost to Cyprus later on, as the West Bank and Gaza were. The other difference is that the Palestinians occupied did not have a state and were not part of a larger state. Unlike Cyprus, which continued to exist, the British Mandate had expired, meaning there was no longer any state there. So Palestinians occupied in the West Bank and Gaza by Jordan and Egypt were not part of a state, while Northern Cyprus was part of a state, which is a difference as well.

Please let me know if you have questions :).