The confusion arises out of different terminology that some people use due to misconceptions about what a US "visa" is.
Technically, the "visa" is what some people call the "visa stamp", which is the physical sticker that is placed into the passport. A US visa is solely for traveling to the US to apply to enter. A US visa only has to be valid on the day of entry (for example, you can use a visa to enter the US on the day before it expires, or even on the day it expires).
After entry, how long you can stay in the US is determined by your "status", which lasts until the date on your I-94 that you are given on entry (which is electronic nowadays), and as long as you continue to satisfy the conditions of your status (e.g. for F-1 students, having a valid I-20 and continuing studies). Your visa's expiration date is completely irrelevant after entry.
This is very different from how some other countries work. In some other countries, your visa has to be valid during your stay. As a result of familiarity with how other countries do this, or as a result of popular misconceptions, people (even most Americans) will often incorrectly believe that you must have a valid "visa" to legally stay in the US, and that the visa is somehow a proof of your legal status.
There are many cases where people in some kind of long-term status will remain in status long after their visa expires, or will extend their status beyond their visa's expiration, or will change their status to a status that they did not have a visa for. For example
- F-1 students are admitted not until a specific date, but for "D/S", which means they remain in status indefinitely as long as they maintain their status. But F-1 visas are only for a limited length of validity, depending on nationality; for some nationalities it is one year or shorter.
- H-1b workers are admitted for the duration of their H-1b petition, but the petition can be extended while in the US. Their visa will expire at the expiration date of the original petition.
- F-1 students commonly change status while in the US to H-1b status. They only have their F-1 visas, and not H-1b visas.
In these cases, the person would not have a valid visa matching their current status in the US. If they ever want to leave the US and return to the US, they would need to apply for a new US visa from a US consulate abroad (it's generally impossible to get a US visa inside the US, because visas are only for entering the US).
For people who have the misconception that you must have a valid "visa" to legally stay in the US, the idea that you can have valid status in the US for long periods of time without a valid visa, until you need to leave the US, seems wrong. So instead, they use a different set of terminology that seems to be more consistent with their misconception:
- They refer to their status in the US or their I-94 as their "visa". They will say they "extended their visa" or "changed their visa" to refer to an "extension of status" or "change of status", respectively.
- They refer to the act of getting an actual visa from the US consulate as "visa stamping". They incorrectly believe that they already have a valid "visa" corresponding to their status, it's just not "stamped".