The Machine Learning Engineer Nanodegree program is the most general of the three programs. It offers a great foundation, and is an excellent choice for anyone pursuing a career in a field where machine learning techniques are used. However, the curriculum is not as advanced as the other two programs, and it does not specialize to the same extent.
The Machine Learning Engineer program is not an official prerequisite for either the Self-Driving Car or Robotics programs, though it may be beneficial to some students to complete this program first, depending on your existing knowledge and experience.
The Robotics program provides an introduction to various aspects of robotics including perception, localization, path planning, and control, as well as the Robot Operating System (ROS). All of the techniques required to complete the projects in the Robotics program (including machine learning) are taught as part of the program.
The Self-Driving Car Nanodegree is a specialized robotics program; it uses robotics concepts and applies them to a self-driving car. If you are interested in robotics in general beyond the field of self-driving cars, then the Robotics Nanodegree Program is for you.