I have gone through different questions/articles on Message Brokers and ESBs(Even on stackoverflow). Still not a clue as what is the CLEAR demarcating difference between an Mess
IBM has ever since changed the names of their ESB offering, so I wouldn't go into the names or vendors.
ESB allows business information to flow between disparate applications across multiple hardware and software platforms. ESB is more of a middleware layer which holds application connectivity logic and minimal to NO business logic. This allows applications to do what it does best without worrying about embedding any connectivity logic on how to interact with other N number of applications that require the data from it. ESB architecture attempts to solve the point to point spaghetti mess in an enterprise.
ESB and Message Broker is kind of synonyms to each other, however as one of the responses above has highlighted that Messages Broker pattern is a portion of the larger ESB domain. The letter "B" in ESB is analogous to the bus(hardware) in computer architecture. The bus on the motherboard or in a computer connects various components for the functioning of the computer. ESB is a software based bus connecting various services in an enterprise. Hub and spoke is one of the patterns supported by ESB architecture. In the monolithic world, each vendor has their own high availability deployment architecture to ensure the ESB is available. The recent offerings of any ESB vendor is in terms of microservices based deployment model or hosted in their own cloud known as a iPAAS. So this ensures that Bus will never fail or fail temporarily with self healing based on your deployment model selected. With microservices based deployment or iPAAS, ESB's now have auto-scaling capabilities(horizontally or vertically) with features varying based on the vendor selected.
For a very high level capabilities that ESB provides, you could go through the following link => https://en.wikipedia.org/wiki/Enterprise_service_bus