Think of Israel as the equivalent of the USA, and think of Judaism not as a religion, but as a Legal System, and thus as the equivalent of US Law. Now the categories are equivalent as such:
1) Natural-born Jew = Natural-born US Citizen. They have all the rights and obligations of a US citizen, including voting, and may pursue the US Presidency. In extreme circumstances (i.e. acts of treason for which they have been found guilty by the judicial system), they are subject to punishment of anything from imprisonment up to and including state or federal capital punishment, but they cannot be stripped of their US Citizenship.
2) Ger Tzedek (lit. "Righteous Covert") Jew = Naturalized US Citizen. They have all the rights and obligations of a US citizen, including voting, but subject to the restriction of pursuing the US Presidency. In extreme circumstances (i.e. acts of treason for which they have been found guilty by the judicial system), they are subject to punishment of anything from imprisonment up to and including state or federal capital punishment, but they can also be stripped of their US Citizenship (and thus deported).
3) Ger Toshav (lit. "Resident Alien") = Green Card holders. These are Foreign nationals who are not US Citizen but are Legal US Permanent Residents holding a valid US Permanent Resident Visa. This grants them a right to legal permanent residency in the USA. They have all the obligations of a US citizen (i.e. pay tax, follow the law, etc...) but they do not have all right, though they do have most rights. They have the right to reside permanently, right to work, etc... The main rights they are excluded from are the right to vote and the right to pursue the US Presidency. In the most extreme of cases, they cannot be regarded as having committed treason against the USA since they are non citizens, however, for acts which would be treasonous if they had been a US citizen (for which they have been found guilty by the judicial system), they are still subject to punishment of anything from imprisonment up to and including state or federal capital punishment, but they can also be stripped of their Permanent Residency (and thus deported).
4) Goyim (lit. "Nations") = Any and all Foreigners who is neither a Natural-born US citizen, nor a Naturalized US Citizen, nor a Green Card holder. This class of people includes Foreign Tourists on Visa Waivers, Foreign Tourists on Tourist Visas, Foreign Business people on Visa Waivers, Foreign Business people of Business Visas, International Student on Student Visas, and all other people on other visa types etc... It also includes Assylum Seekers awaiting Refugee Visas, Refugees on Refugee Visas, and finally people residing illegally in the USA without any visa or permit. This entire class of people termed "foreigners" have only non-privileged basic rights while in the USA. Those who are in the USA illegally without any visa or permit have even less rights than the basic rights, since they are in the USA illegally. Whatever the case, all foreigners in the USA, whether they are in the country with or without the appropriate visas or permits, have no right to work (unless on a current working visa), no right of residence (beyond the time granted in their visa), no right to welfare, no right to vote, no right to seek the presidency. These lack of rights comes with the benefit of having no real obligations to the USA other than ensuring they don't break the law as visitors that they are. They don't have to pay tax (because they shouldn't be working, unless they're on a working visa, in which case they pay tax but at a higher rate). Good and services tax can be avoided by them if they are travelling ("duty free" purchases). If they break any US laws during their visit, however, they may be deported, and the laws they break need not be the extreme of cases. They can also simply be refused entry into the USA.
The different categories of status in Jewish law of people inside Israel also imposes different rights and obligations depending on the category one falls into. Including who can eat a carcass (Ger Toshav and Goyim), who keeps Shabbat (natural born Jews and Ger Tzedek Jews), who can marrying a Kohen (only a natural born Jew can marry a Kohen, though if you were born to a Ger Tzedek Jewish woman after she converted, then you yourself are a natural born Jew, and you can marry a Kohen), etc...