The idea with striving for solutions is to bring us closer to some imagined utopia, even if that might lead to a worse situation in the short term. This view does not just consider attainable alternatives, but includes fanciful benefits in it’s trade-offs, that are far away in theory land. Obviously the benefits of some utopian theory will always outweigh short term downsides and destruction. Conversely, striving for improvement does not look at theoretical benefits that are predicted by some utopian theory. It only considers attainable alternatives in the real world. It is a way of deciding upon the best of the currently available options, as a means to gradually achieve better and better conditions.
Applying this to the aforementioned example of gun control. The vision seeking improvement wants people to have guns, this means sometimes accidents happen or good people get shot, but it is the least deadly alternative. The vision seeking solutions dreams of a perfect world where nobody gets shot, ever. Striving for this unattainable solution leads to a worse situation, which kills millions more people. But it is not the actual real world consequences that matter, but that this policy is closer to an envisioned utopia.