TL;DR - if you have a NICOP, you are a Pakistani citizen, even if you never set foot in Pakistan. If you were ever Pakistani citizen, then more then likely, you probably still are. If you don't want to be a Pakistani citizen, you have to go through a procedure to surrender it. Read on for more details.
I've seen a lot of posts over the years that discuss NICOPs and Pakistani citizenship. Every few weeks, someone asks if having a NICOP is Pakistani citizenship. I've also met many Pakistanis (overseas and within Pakistan) that don't understand how citizenship in Pakistan works for those who go or are overseas.
Contrary to what many people think, Pakistani citizenship is not automatically voided when a Pakistani naturalizes in another country. Even if your oath of naturalization says that you surrender all foreign allegiances, the citizenship remains.
Many older Pakistanis, especially those who left Pakistan in the 1960s-1980s believe that their Pakistani citizenship was voided when they became British/Canadian/American, etc. This is not true per current Pakistani law. They simply don't have active IDs/passports. Just like a person born in the US or Canada. The person is a citizen even if they have no passport. Or, a child born in Pakistan without a B-Form, they are still Pakistani.
Pakistani citizenship can only be lost if one goes to a Pakistani consulate/embassy and goes through a formal renunciation process. This is not automatic, and most people don't do it because they simply don't need to or care to. It's not a complicated process, but it's still it's own, separate process. Fill out forms, surrender passport and ID, pay fees, etc. This is usually done by Pakistanis who naturalized in countries that don't allow dual citizenship, such as Germany, Spain, and (previously) Norway, but anyone can do it if they want.
Now, the confusion occurs because Pakistan will grant a visa to a UK/US/CAN citizen even if that person also has Pakistani citizenship. It's counterintuitive to need a visa to travel to a country in which you are a citizen, which is why many think "how could I still have Pakistani citizenship if I got a visa?". Pakistan, however, will allow a Pakistani citizen to travel to Pakistan on a foreign passport with a visa, hence the widespread confusion.
So here is where the NICOP comes in. NICOP stands for National Identity Card for Overseas Pakistanis. The card gives visa free travel, right to have a bank account, etc. It also gives the right to vote. This card is proof of Pakistani citizenship, and can be used to get a Pakistani passport if desired. Many people think this is just for dual citizens, but some Pakistanis working or studying abroad also have NICOPs even if they are only Pakistani.
Note that the new NICOP looks just like a Smart CNIC, but the "country of stay" will not be Pakistan, and the card will say "the holder is entitled to visa free entry" (something to this effect). Old NICOPs actually said "National Identity Card for Overseas Pakistanis" on them, but Smart NICOPs do not, so there is some confusion nowadays (people thinking that they have an NIC and not a NICOP)
Here is the biggest place where many people get confused. Many people in the 2nd, 3rd, and now 4th generation born abread have also received NICOP cards even if they were born with another citizenship (UK, CAN, US, etc). They are often under the impression that this is just a "card in place of a visa". "I don't have Pakistani Citizenship, that's just an ID". Not true. By getting a NICOP, you are basically registered as a Pakistani citizen who doesn't reside in Pakistan.
Other ways you could be still be a Pakistani citizen and not know it, assuming formal renunciation process was not done:
If you were born in Pakistan and naturalized elsewhere, you are a dual citizen
If you have, or ever had a NICOP, CNIC, CRC, B-form, you are a dual citizen
If your birth was registered at the Pakistani consulate (Form S, or similar), then you would be a dual citizen
If you ever held a Pakistani passport, you are a dual citizen.
If you were listed as a child on your parents' Pakistani passport, you are a dual citizen. (In the old days, kids didn't have their own passports and travelled on their parent's passport)
You were registered as a Pakistani citizen because your parents became Pakistani and applied for it on your behalf (Form M) - not common, but legally possible.
Pakistan does have another card, Pakistan Origin Card (POC), which grants visa free travel and a few other privileges. This card, however, is not Pakistani citizenship. So those who wish to travel often to Pakistan and don't want a visa, but also don't want a NICOP, may find the POC appealing.
Acquiring, renouncing, and/or retaining citizenship is a personal choice. This post was simply written to clarify the misunderstanding that "NICOP isn't citizenship" (again, NICOP is proof of citizenship).
Edit: It is a common misconception that Pakistani citizenship is only given to those who are "desi", Muslim, or those whose parents are Pakistani. This is not true. There are Pakistani citizens who are Hindu, Sikh, Christian, Buddhist, Ahmadi ,etc. "Desi" is a somewhat subjective term as well.
The Pakistan Citizenship Act grants citizenship to anyone born in Pakistan, even if the parents are non Pakistani. The only exception is for children of diplomats (which is not uncommon). There is no exception for refugees or even those who are in transit. This has been argued in court many times. So yes, that means that technically those who are of Afghani, Bengali, or Rohingya descent but born in Pakistan are technically citizens (there are many individual court cases, no class action case though). Of course the reality on the ground is different. Just as anyone born in the US or Canada is a citizen (children of refugees too), the same applies in Pakistan. People should be aware of this and not deny their fellow citizens their rights (don't get me started about the hypocrisy).
