What is the difference between US permanent residence and US citizenship?
Permanent residence (a "green card") grants the right to live in, leave and reenter, and work in the US. It does not grant, for instance, the right to vote in U.S. elections.
Permanent residence may be deemed abandoned if the US government believes that the permanent resident has not maintained sufficient ties to the US to demonstrate intent to keep it. It can also be revoked if, for instance, the permanent resident commits certain crimes.
Citizenship includes all those rights, plus the right to vote and certain other rights. Citizenship cannot be deemed abandoned even if the citizen resides abroad for long periods of time without strong ties to the US. It can be taken away, but normally only if the naturalized citizen can be proven to have misrepresented something during the naturalization process (or does something which could also cause removal of citizenship to a US-born citizen, such as fighting with a foreign army against the US)
What is naturalization?
Naturalization is the process of applying for US citizenship. A citizen who obtained US citizenship by going through this process rather than birth in the US is said to be "Naturalized."
Are there other requirements for naturalization to US citizenship aside from having had a green card for the required amount of time?
Yes. Possession of a green card for a certain period of time (three years for a foreign national who obtained permanent residence based on marriage to a US citizen, five years for foreign nationals who obtained permanent residence through any other method) is only one of several requirements for naturalization. Not everyone who has a green card is eligible for citizenship.
Is the naturalization process always needed to obtain US citizenship?
There are cases where individuals in certain situations can get citizenship without going through naturalization.
Children born overseas to US Citizen parents can obtain citizenship simply by applying for a US passport and showing evidence of parentage and of the parents' citizenship (birth certificates of the child and two US-born parents, for instance).
There are various other situations, although rare, where various laws bestow US citizenship on individuals automatically by operation of law (birth in the Panama Canal zone during certain periods is among these circumstances).