No, they're actually different browsers, though both came with windows 10.
That makes IE11 even worse since it hasn't abandoned compatibility and still performs incredibly badly. Maybe Microsoft is deliberately sabotaging it to move people towards "Edge".
Microsoft is stuck here: they want to move on to modern web standards, but they can't afford to piss off their corporate customers.
Their solution is to split the web browser, shipping Edge for the consumer market (and the modern members of the business market) that wants to interact with the modern web, but still continuing to provide IE11 along with the OS to keep their corporate dinosaur customers happy.