The succincter version:
No matter the wording they use in their Acts, when Congress causes the US military, by acting through the Executive, to act to damage a foreign or rebellious power of any kind, they are declaring war by definition. The men who wrote the Constitution wouid have expected no less of a reaction than war from any foreign power they attacked or defended against.
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And you can't claim that authorization isn't an order. Any President who didn't use force after being authorized to use force by Congress is playing dangerous, trans-Constitutional games. Authorizing force is a political act and can't be construed as neutral and and non-binding by the Executive--no sensible person would interpret Congress sending you a law authorizing use of force as anything other than commanding use of force. A power of command the Framers intended Congress and no other to possess. And to state however they wanted.