Visa and status are often used interchangeably, but are actually different.
Jane is a college student whose application for an F-1 visa has been approved by a US embassy. The visa is valid for six months. This means Jane can fly to the US anytime during the six-month period (A student visa holder cannot arrive more than 30 days before school begins). However, her visa doesn't guarantee her entry into the US. At the airport, an immigration officer will inspect her visa and other paper work before making a decision. Since everything is fine, the CBP officer stamps Jane's passport to establish her status as an academic student, and issues her an I-94 card. So now Jane is legally in the US under F-1 status.
After Jane's F-1 visa expires, she still remains in legal F-1 status.
Two years later, Jane completes her Master's degree and receives a job offer. Her prospective employer files I-129 to apply for an H1B visa for Jane. Upon approval, Jane's status has now changed from F-1 student to H1B temporary worker. But she doesn't have an H-1B visa on her passport.
If Jane wants to visit her family back in her home country, she needs to apply for a new H-1B visa in order to return to the US, even if she is already in H-1B status.
