Rxswift observable bind(to:) vs subscribe(onNext:)

Look at the implementation of bind(to: )

public func bind<O: ObserverType>(to observer: O) -> Disposable where O.E == E {
    return self.subscribe(observer)
}

Subscribe is called inside.

Regarding your statement

As far as I know, observable won't produce value unless a observer subscribed on it

This is only true for cold observables. Let me quote from RxSwift docs

When does an Observable begin emitting its sequence of items? It depends on the Observable. A “hot” Observable may begin emitting items as soon as it is created, and so any observer who later subscribes to that Observable may start observing the sequence somewhere in the middle. A “cold” Observable, on the other hand, waits until an observer subscribes to it before it begins to emit items, and so such an observer is guaranteed to see the whole sequence from the beginning.

Since I stumbled upon this question trying understand the difference between those two I would like to add that for bind:

In case error occurs in debug mode, fatalError will be raised.
In case error occurs in release mode, error will be logged.

The approach is different for subscribe(onNext: which allows to explicitly handle onError: with custom handling (same for onCompleted onDisposed).

As @chriswillow already answered both bind and subscribe(onNext: do subscribe to an observable.