A realistic drawing is a highly-detailed photo realistic representation from a photo. They have a timeless and classic quality. These drawings have a great amount of detail and therefore take a longer amount of time to complete. One reference photo is preferred, but more may be used in order to achieve a desired outcome. For example, two photos are used when morphing two different animals together, or when a different background is wanted in place of another. This can be finished in pencil.
An illustrative drawing has more of a creative style behind it. It may look more whimsical and have a more “storybook” feel to it. I use more of my creativity to personalize the drawing and make it truly unique. Several reference photos from your collection or my own may be used to build up this piece. This can be finished in pencil, colored pencil, or pen.