The main difference between ESB and EAI is not a clear mistake.
Having said that, if the ESB Bus fails, yes, that is the point of failure. Ultimately, these are just applications in your infrastructure and whether they are a single point of failure or not, depends on their deployment (for example, clustering), and not on the basic conceptual integration template.
Personally, I would classify ESB (Enterprise Service Bus) as an EAI (Enterprise Application Integration) type. Many companies trying to sell you a product instead of a concept will argue differently.
ESB is just a new template for EAI instead of Hub-Spoke. I would not be too carried away by differences. When you dig into them, they are few and far between.
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