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None of Adobe's tools use the same rendering model, each has its own brush format and brush features, so not every brush works in every application.
That is, you can't use an Illustrator brush in Photoshop or in Sketch, or a Sketch brush in Photoshop or Illustrator. Photoshop's rendering model just can't handle what Sketch can, it works in a very different way. This is why when you create a brush in Capture, you have to select what tool you are going to target. If you're ultimate goal is to use the brushes in Ps, then you'll need to limit yourself to the Ps targeted brushes when you get to the Style section (look for the Ps icon on top left of the section, after the Photoshop Sketch brushes).
When you save a brush, you're taken to a screen where it can be edited/named). It's also where you can see which brush work with each application. The top three are for Photoshop Sketch. If you scroll down you'll see the brushes for Ps and Ai. When you save, save for the app in which you'll use it. Let me know if that clears things up for you.
Try this with one of your brushes:
Go into your Library and choose a brush
Tap the edit icon (square with a pen); that will open a visual list of brushes
If you want to use a brush in Photoshop, choose one of those brushes (tap the circle to check it), name it, and Save. It will save to your library as a Photoshop Brush and as soon as it syncs you should be able to open it there from your Library panel.
Let me know if that clears things up for you.