If you set a background image, the image class can be used to change how it is stretched.
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Custom class is exactly what it says, it allows you to define a class that is applied to the category. In Lavender, this is used to position blocks in certain arragements (e.g. 3 to a row, 4 to a row, etc). In Persona, they are not used, but you can still used them if you wish to apply special styling to certain category rows.