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Unfortunately, there isn't a way to apply different styles for the same controls in the RadSpellChecker. This means that every control of a given type will have the same style inside the control.
If you want to style the TextBox control you can base your own style on the 'TextBoxStyle' which is provided by us and is placed in System.Windows.xaml file. This file is a resource dictionary which contains styles for some of the native MS controls. Here
you can find the full list of styled controls.
Anyway, the TextBox on which you want to change the Foreground property is in ReadOnly state, but unfortunately even you set that property in its Template's VisualState on the element in the control template which is responsible for displaying the text, the internal MS control TextBoxView is not updated. It gets only the TextBox's Foreground property value which is set through the style setter or locally. This is a limitation of the TextBox control.
I hope this information will be helpful.
If you need further assistance, please contact us again.