Mechatronics Engineering

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 vending 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.