"if (student.name === search)" — why does this work?

In the video, this snippet of code is used to check if the user's search term matches a name in the student record:

for ( var i = 0; i < students.length; i += 1 ) {
  student = students[i];
  if ( student.name === search ) {
    message = getStudentReport( student );
    print(message);
  }
}

I don't get why would "if (student.name === search)" work.

Let's say that we're making the first loop, where "i = 0". That would make "student.name" in effect be "students[0].name", which maps it to a specific student each round (in this case, it's "Dave".)

So if during the first search, where "i = 0", I look up "Jody", using the "if (student.name === search)" code, wouldn't it return with "(Dave !=== Jody)"?

Which is to say, the program will only print out a student's name if the name you look up during your nth search matches the student in exactly nth object in the array.