It's important to realize that the words “visa” and “green card” can mean more than one thing. In fact, while in some cases their meanings are quite distinct, in other situations, their meanings overlap a bit.
Let’s start with the narrow meanings. A visa gives you the right to present yourself at the border or port of entry and seek entry to the United States. (Ultimately, the U.S. Customs and Border Protection officer at the border or airport makes the final decision whether to allow you into the country. Nonetheless, having the visa is normally a good sign that you'll be allowed to enter.)
Physically, a visa usually appears as a stamp in your passport. 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.
“Green card” is a slang term. In the narrowest usage, it is the plastic photo identification card that you receive when you become a U.S. lawful permanent resident.
Now, for the broader meanings. The word visa may also be used in situations involving immigrants who are already in the United States and won’t need an entry visa. That is partly because someone in the deep dark offices of the U.S. State Department may have to allocate a visa number to these immigrants, though the immigrants may never even know it. When you read discussions about your “visa eligibility” or “visa availability,” they are not referring to the actual visa that you pick up overseas, but to the broader, theoretical visa that the State Department will allocate to you.
The term green card also takes on broader meanings at times. It is often used to refer to lawful permanent residence or lawful conditional residence. When you see the term “green card application,” it is actually referring to one of the application processes (adjustment of status or consular processing) that could lead to obtaining U.S. residence.
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. 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.