There’s a slight difference between a robot company and a robotics company. The term “robot company” refers to the actual robots built. An example of a robot company would be iRobot, the company which manufactures the Roomba.
In contrast, “robotics company” refers to a company that builds the systems and technology behind a robot, not just the robots. Nachi Robotic Systems, Inc. is a company that produces robots, robotic technology, and more.