As a long time teacher, I have, sadly, had dozens (if not hundreds) of students who simply showed up for class each day without bothering to pay attention in class or complete many of their assignments. They are students. A learner is a student who wants to absorb as much knowledge as possible and still seek more.
I would say that a student is someone who attends school. They might be a good student or a bad student. They might go to class or they might not but they are still a student at that school. A learner is someone who is interested in the information. They might make wonderful grades or they might not. The learner cares about gleaning the information and not necessarily about the grades. Of course, someone who genuinely cares about gathering information isn't likely to fail a course or make poor grades. They will retain the information and build upon it. A true learner is likely to gather more from a course than other students.
A student is someone who is very good at "playing school." They come to class, do the homework, raise their hand when prompted, and do what the teacher asks. The student will do what it takes to earn the desired grade, and no more. A learner, however, recognizes that he/she is there to learn skills and wants to apply those schools in a practical setting. A learner does school activities and work with the knowledge that there is a purpose behind them beyond a grade. He/she will seek new information even if that won't affect the grade at the end of the year.
If there is one, it is that a learner is someone who actually cares about learning and is fully engaged in the process. A student is someone who just shows up to class. A learner is someone who wants to learn and is trying their best to do so.