I'll quote a little more of the context that I think is needed for this to make sense.
Strategies are a better choice in situations where the Component class is intrinsically heavyweight, thereby making the Decorator pattern too costly to apply. In the Strategy pattern, the component forwards some of its behavior to a separate strategy object. The Strategy pattern lets us alter or extend the component's functionality by replacing the strategy object.
For example, we can support different border styles by having the component defer border-drawing to a separate Border object. The Border object is a Strategy object that encapsulates a border-drawing strategy. By extending the number of strategies from just one to an open-ended list, we achieve the same effect as nesting decorators recursively.
All this is saying is that both patterns can be used to add behavior to your base component, and that with Decorator, to add multiple behaviors, you can nest the decorators, while with Strategy, you need to use multiple strategies.
You're right that strategies are generally more independent of the main component than decorators, but it is possible for them to be aware of the component. And to use the Strategy pattern, the main component is aware of the existence of strategies, where that's not needed with Decorator.