Traditional US Army usage (I don't have the definitions handy) was that a Regiment was a fixed organization of (predominantly) a single arm/branch, while a Brigade was an unfixed organization combining multiple arms/branches, but that wasn't always true, since a square division in WW1 had 2 brigades of 2 regiments. It is also not true in the current organizations, since each of the three BCTs have a fixed organization. The Multifunctional and functional support brigades have an unfixed organization, but at least the functional support brigades are predominantly of one arm.
It also depends on the size of your regiment, since some nations' regiments are only battalion sized.
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