What's the difference between mechatronics and robotics?

In simple words, all robotic systems are mechatronic systems. But, all mechatronic systems aren't robotic systems.

Mathematically, robotics is the subset of mechatronics set. 

Robotics is a specific branch of mechatronics that requires the knowledge of,

• Dynamic system modeling and analysis
• Control engineering
• Signal conditioning
• Sensors and actuators
• Hardware interface
• Path programming
• Kinematics and so on...

As you can see, even a mechatronic system requires the above mentioned elements. However, it differs from a robotic system in terms of functionality and the use case. For example, coffee wending machine, airplane, washing machine, automobile etc. are all mechatronic systems, which belong to different use cases. However, robots are unique in terms of their functionality and use case.