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Brand guidelines go deeper into brand, its characteristics, communication, target group, slogans...stuff like that. Design manual is just about the logo and its usage. This one is very simple.

I have done the same thing as you do "brand manual", but I have called it 'brand guidelines'. there may be disputes here depending on the region. 😀. and brand guidelines that I do related to the use of assets, do and dont, placement, color and font used.