The words “visa” and “green card” can mean more than one thing, and can even overlap a bit.
Let’s start with the narrow legal meanings.
A visa is a document prepared by the U.S. Department of State (DOS), which gives someone the right to present themself at a U.S. border or port of entry and seek entry. (Ultimately, the U.S. Customs and Border Protection officer at the border or airport makes the final decision whether to allow someone into the country. Nonetheless, having the visa is a good indication that entry will be permitted.)
Physically, a visa usually appears as a stamp in one's passport. If and when you receive instructions to go to a U.S. consulate to pick up your visa, it means that you will be getting this stamp or an equivalent document that allows you to enter the United States.
An "immigrant visa" allows a person to become a permanent resident immediately upon U.S. entry; he or she will receive a green card soon thereafter. A "nonimmigrant visa" is only temporary. The person will need to leave by the date shown on the I-94 that he or she is issued at entry.
"Green card" is the slang term for the plastic photo identification card that someone receives upon becoming a U.S. lawful permanent resident. This includes cases where the person recently entered the U.S. using an immigrant visa, as well as cases where the person applied for permanent residence from within the United States. The term "green card holder" is often used to for lawful permanent residents as well as lawful conditional residents, though the latter's status expires in two years (as discussed below).
In most cases, nonimmigrant (temporary) visas, such as a B-2 tourist visa, an H-1B temporary specialty worker visa, or an F-1 student visa can be obtained only at an overseas U.S. consulate.
However, someone already in the U.S. legally can apply to U.S. Citizenship and Immigration Services (USCIS) for a "change of status," for example from F-1 to H-1B. Importantly, receiving that right to be in the U.S. does not mean the person receives an actual "visa." Remember, a visa is an entry document, and can be issued only by the DOS. So if, for example, the H-1B worker who got a change of status leaves the U.S., he or she will have to make a stop at a U.S. consulate to get an actual visa with which to reenter the United States.
Immigrant visas (such as marriage- or employment-based permanent residence) are also obtained at U.S. consulates around the world. But here too, someone already in the U.S. (in most cases, legally) may be able to "adjust status" and get a green card (permanent residence) without departing.
Nonimmigrant visas are temporary. They usually expire within a few years, though many can be extended or renewed. (See How Long Will Your U.S. Visa Allow You to Stay?)
A lawful conditional resident's green card also expires, within two years. (People who obtain green cards based on new marriages or as investors in category EB-5 receive only two-year conditional residence at first.) Close to that expiration date, the person must submit an application proving that he or she deserves lawful permanent, not just lawful conditional residence. (See Why Some Marriage-Based Green Cards Are Conditional.) If that isn't approved, the person loses status and most likely all right to be in the United States.
A permanent resident's green card also carries an expiration date, usually of ten years. This is NOT, however, an indication that the person's status expires or must be re-proven then. Lawful permanent residence is truly meant to be permanent, unless the person violates the laws and becomes deportable. However, the authorities want to make sure all permanent residents get a new card regularly, for which one must submit an application on USCIS Form I-90.
To add to the confusion, the word visa may be used in situations involving immigrants who are already in the United States and won’t need an entry visa. Only a limited number of green cards are allowed in certain categories every year, and the government tracks these as "visa numbers." Someone in the back offices of the U.S. State Department must allocate a visa numbers to each immigrant when a number is available in their category, though some of the immigrants may never know it, much less need an entry visa.
When you read discussions about your “visa eligibility” or “visa availability,” they might refer not only to the actual visa that you pick up overseas, but to the broader, theoretical visa number that the State Department will allocate to you.
Green Cards Don’t Work Like Tourist Visas
Don’t expect a green card to work as a frequent travel pass. A common misconception about green cards is that they allow you unlimited travel in and out of the United States without the hassle of reapplying for visas.
The result of this confusion is a common practice by overseas family members of U.S. citizens or residents who want to be able to pop in for impromptu visits--they sometimes apply for green cards. But if your plan is to maintain your primary home in another country, the U.S. government may eventually figure this out and cancel your green card. The legal term for this is that you abandoned your U.S. residence. (See Nolo's article on issues when traveling with a green card.) You might have to start over and apply for another one; provided, of course, that you intend to make the United States your primary and permanent place of residence.
If, for example, you are married to a U.S. citizen or resident but plan to live in your home country for much of your early marriage, or to shuttle back and forth, you may want to wait until you are really ready to settle in the United States to apply for your permanent resident status.