Leaven Vs Fed Starter

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I am new to baking sourdough. Some recipes ask that you make leaven from fed sourdough starter and others just use the fed sourdough starter directly. I just fed my started about 7 hours ago, it has more than doubled in size, is bubbly and passes a float test. The recipe I would like to try says to make leaven from "fed/refreshed starter" can I skip this step and just use the starter directly? Is it not kind of the same thing?

You can do either one, some prefer to make a levain as an off-shoot of their starter and some use starter straight from the jar. 

If you are using your fed starter as levain just make sure you don’t use all of it because you won’t have any starter left.  This is one of the reasons people will make a levain as an off shoot of their starter, they won’t accidentally use all your starter and then have to make a starter again from scratch.