I've been some confusion about how H-1Bs relate to foreign students in US universities. I've said this before: the H-1B is the primary visa that foreign students already in US universities get after they graduate.
"Employers of F-1 students under OPT often file petitions to change the students' status to H-1B [..] Many times, [..] work authorization would expire prior to the student being able to assume the employment specified in the approved H-1B petition, creating a gap in employment."