The US government gets money in mostly by taxes and by borrowing. How the money comes in doesn’t have much to do with how it’s spent…if they want to spend billions on foreign aid they do it the same way as if they want to spend billions on military hardware or domestic infrastructure or anything else they want to spend money on. Unless specifically restricted by legislation, all the revenue just goes into one bit “pot” to spend from.
It gets approved by Congress; the US constitution restricts, with a few very specific exceptions, budgeting to Congress. So they have to pass a law that says “We authorize the executive brand to spend $X on Y purpose.” Then the executive branch (President, Department of Y, etc.) actually spends it.
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