It is the responsibility of the visitor to ensure that the INS official at the border assigns the B-1 classification. This should be clearly stated in the invitation letter. Individuals from many countries do not need a visa if they are coming to the US for business or pleasure for less than three months. This is a green card presented to passengers on the airplane - which they fill out. At the port of entry INS officials stamp the card with visa type and length of stay is established.
Green card is stapled to passport, which INS officials remove from passport on return flight.