Being a learner represents a dynamic relationship with some sort of content, resulting in growth and new understandings. In the best situations, there is an excellent fit between a teacher, a learner, and the content. The learner is thus deeply engaged with the material, invested in the desire to demonstrate growth. Learners are typically intrinsically motivated, and good teachers facilitate this learning by adapting instruction, content, and activities in a way that continues to foster interest.
It is possible to be a learner without even having a teacher. Many people have diverse interests that they develop themselves. From learning to play guitar to learning how to edit videos to learning how to bake pastries, people often demonstrate that interest and motivation are key to being a true learner.
A student, on the other hand, is typically considered to exist in a traditional school setting. Students typically meet in groups of approximately same-age peers and often learn the same things at the same times, regardless of interest. Because of the nature of education in America, students are often taught to perform for tests and other assessments. Some people become quite good at being students, excelling on tests and without ever truly learning the material. Students memorize well yet sometimes cannot manipulate what they have memorized to adapt to new scenarios.
Looking back across a long and diverse range of educational experiences, most people can recall classrooms where they were students and others where they truly became learners. When material is relevant, appropriately challenging, and engaging, individuals are more likely to become great learners.