When i think of the word 'session', i think in terms of each individual user as a session
The term "session" in this context means unit of work or business transaction.
In Stateless and Singleton beans, a new session/business transaction is opens when a new request arrives,
and it lives until the response it sent back to the client. (session-per-request pattern)
For Stateful Session bean the business transaction could implies several client requests. From the Stateful bean's perspective, a client is a proxy that sends the requests to the same stateful instance.
Edit (too long for comment)
I think Application Bean could probably be a good name, in fact they are good for storing application settings, but the key point is why they are called Session Bean.
In this context "session" is the period of time the business transaction executes. For Stateless and Singleton this period matches with the request/response cycle.
...If that singleton session bean is for across application, shouldn't it not be called a session bean
The fact that a Singleton maintains its state between client invocations doesn't means that the session-per-request model doesn't applies. Every Singleton reference used in your application is a client, when a client makes a request a new session is created.