Electronics is a sub-branch of electrical engineering. Until around the 50s, electrical engineering consisted only of power systems, machines and other heavy electrical equipments. But with the advent of semiconductors, electronics started becoming more prominent and by the end of 60s, it became so big that new departments started cropping up. IITs and most of the American universities decided that they could handle such big departments so they decided not to divide. You will hardly ever find electronics department in US.
When someone says that he is an electronics engineer, he is necessarily an electrical engineer but an electrical engineer could be electronics engineer or controls engineer or communication engineer or RF engineer or power systems engineer or power electronics engineer, etc.
So, I actually quite like the system at IITs because it gives more freedom to the students to choose what they want.
Electrical engineering does not mean power engineering that most people in India believe it to be. It has a much broader definition.