The only similarity between magic and science is that both have rules. The rules indicate the types of moves which are permitted. From humble beginnings, both domains have expanded into powerful forces.
These are the main differences.
1. Predictability
Science tries to achieve predictive success.
Magic is the opposite. Every spell cast will have unintended consequences.
2. Book-keeping
Science is the ultimate book-keeper. The laws of conservation and thermodynamics keeps track of all energy, matter and information.
Magic doesn't really bother keeping track of anything. A rabbit can be conjured out of thin air without disrupting the laws of magic.