A Visa is the document placed in your passport by the US Embassy or Consular official. This document permits you to enter the United States. It may be valid for 6 months or a year or longer. You may be able to use it to enter the United States many times or just one time. If your visa expires while you are in the United States, it does not mean that you are out of status or “illegal”.
Non-immigrant status is granted when you arrive in the United States. The USCIS officer at the point of entry (airport or border) will issue a Form I-94. This form will indicate your non-immigrant status, H-1B, J-1 or dependents H-4 or J-2. He/she will also indicate an expiration date. For H-1B holders, this is usual the expiration date on you approval notice. For J-1 holders, the Form I-94 will be marked D/S for Duration of Status. For researchers, the duration is 3 years within a possible 6-month extension to complete the ongoing activity.
Therefore, it is a Visa that gets you the point of entry in the US and the Non-immigrant Status, which allows you to remain in the US