Overall, Ds start more wars and Rs end more, but GWB started a couple and D's ended both. The clearest statistic is that where the US controls the start date and the finish date of the war, and the war has sufficient duration, then neither party will admit to error by ending a war it started. I'm not going to claim gospel truth for this but it does appear to be a trend.
The War in Vietnam follows this trend, it was started by JFK (D), continued by JBJ (D), then Richard Nixon (R) tried to win it then allowed a peace negotiation, "peace with honor". The Iraq War was started by GW Bush (R), and ended by Barrack Obama (D) The War in Afghanistan was started by GW Bush (R) and ended by Biden (D)
The present conflict in Ukraine started with a coup in Feb 2014 on Obama's watch (D) by Victoria Nuland and the CIA, simmered and then eventually in 2021, Joe Biden (D) was able to send sufficient weapons to the government in Kyiv to attack Donetsk and get the war going properly. Donald Trump (R) although willing to use cruise missiles in support of a war started by the Republican GW Bush, had been unwilling to send any weapons to Kyiv to support the conflict started by Obama, Biden, and Nuland, and articles of impeachment were raised by House Democrats against Donald Trump for being unwilling to supply weapons to Kyiv, to use in what was at that time a low-level war against the Russian-speaking regions of Ukraine. I'm not going to claim party allegiance is the controlling factor, but it does appear to count for something.
It is difficult to support the claim that D's start more wars as the numbers are not enough to be statistically significant. By including the attack on Libya and killing of Pres. Gaddafi, that was I understand primarily Hillary Clinton's project, we get 3 started by Ds and 2 by Rs, which isn't significant. I'm not sure we want to include the Democrats in charge when we entered both world wars, because we might argue all night about how much control we had in both instances. So I'll back away from the claim that Ds start more wars.
Why does it matter which party started more wars? Both parties supported most wars and the USA has started more wars than most if not all other major nations in the past century.
Both parties are funded by the MICC (Military Industrial Congressional Complex, as the MIC was originally named). So there really isn't much choice between the parties. Voting for the War in Afghanistan were all 98 of the Senators present and all but one of the Representatives present. Getting a few rebels to vote against numbers like those isn't going to stop any wars. But the President can make a difference.