In practice, in USA, a declaration of war means the whole country is behind the war, including a moral commitment to finance it. It also means allies can rely on American efforts to win the war. The alternative method means the war is not a durable policy, something like tariffs or the East Wing of the White House, here today, gone tomorrow. If Trump loses control of the Congress next January, there will be no further funding of the war. If the Republicans lose control of the government entirely after the 2028 election, the new government might even change sides (e.g. demand regime change in Israel, ban nukes, and demand a return to the 197 border). The willingness of recent (last 80 years or so) presidents to fight wars with declaring them, or to negotiate agreements rather than treaties, means the US can never act as a nation, and never be more than the expression of the whims of whomever is in charge any given day.
