What is the difference between having a crush on someone and loving someone? What is the difference between having a crush on someone and loving someone?
What is the psychological basis of this?
You may find Sternberg's triangular theory of love as useful framework for distinguishing different types of love. Quoting wikipedia, the theory describes types of love in terms of three dimensions:


  
  Intimacy – Which encompasses feelings of attachment, closeness, connectedness, and bondedness.
  Passion – Which encompasses drives connected to both limerence and sexual attraction.
  Commitment – Which encompasses, in the short term, the decision to remain with another, and in the long term, plans made with that other.
  


Using this framework, "loving someone" is the general term, and "having a crush" would be a more specific variant. So perhaps a crush could be conceptualised more in terms of passion and less in terms of long term intimacy and commitment.

Alternatively, you could just look at definitional concepts of a crush. For example, the term "crush" is commonly used in contexts where feelings are not reciprocated. I associate it with younger people (or when seen in older adults, a youthful approach to love). A crush often implies a short term quality, such that the feelings may change from one month to the next.