It looks quite similar to Photoshop's Mixer Brush functionality, although not identical.
In the example below I used a brush tip like this, which I borrowed from one of Kyle's Dry Media brushes, also brush spacing was set to around 3%. You can obviously use any brush tip you want.
Then used it with the Mixer Brush settings shown here, although you can play around with the settings as you please.
And here's an example of the Mixer Brush in action. Please ignore the brush cursor here as my screen recording software doesn't display its size or location properly.
It's also possible to Clean the brush, and use it to smoosh around the paint to allow blending etc.
You can also get a brush to run out of paint by using the Dry Light Loaded preset. Although I note with the Wetness set to Zero, the Mixer is greyed out.
It might be worth your while actually searching for Photoshop tutorials on painting with the Mixer Brush to be honest, rather than trying to compare it with other software like Corel Painter. I'm not an expert on digital painting by any stretch of the imagination. There may be more efficient ways to work with the tool.