None, other than the fact that they're both in the Middle East.
Hate each other
The distance between Jerusalem, Israel, and Tehran, Iran, is 967 miles, (1,556km).
It is roughly 600 miles or 970 kilometers between Israel and Iran at their closest, but 970 miles or 1,5961 kilometers between Jerusalem and Teheran.
There are really no similarities between these countries except on very basic lines such as:All three are regional powers in the Middle East.All three have a substantial Muslim population (around 19% in Israel, and over 90% in Iran and Saudi Arabia).All three have coastlines.All three countries see themselves as the vanguard of the majority religion in the country (i.e. Israel for Judaism, Saudi Arabia for Sunni Islam, and Iran for Shiite Islam).All three have participated in wars in the last decade.
Currently, there is no war between Iran and Israel. There are a number of proxy wars and assassinations which are discussed in the Related Question below.
Iran > Iraq > Israel.
Israel and Iran are two separate countries, with no overlap.
Iran was one of many nations in the region that contributed resources during the so-called "War of Independence" in 1948, but there has never been a direct war between Israel and I ran.
until 1979 with the Islamic revolution at Iran there where an official relationship between Israel and Iran including a weekly flight between the countries. In March 1950, Iran recognised the state of Israel, it was only a De-Facto recognition but one non the lest. that recognition never moved to the De Yoro, which build a very reach relationship between the countries but not known relationship.
Iran.
Both Iran and Israel have a history of hostility with various Arab nations.
-- Western Israel is bordered by Egypt and the Mediterranean Sea. -- No part of Iran borders any part of Israel.
Asia