Lots of things sound similar. Socialized costs and socialism sound similar, and are not similar at all.
You not understanding the concepts or criticism of “trickle down economics” just means you shouldn’t use it as a comparison until you learn more about it, and why it fails.
As a tip, the principal difference is that TDE assumes that cutting taxes for the wealthy will inherently result in business reinvestment, when it clearly does not. This does not rule out all supply-side economics, as renewable energy subsidies and grants have clearly demonstrated. However, demand-side policies are also necessary at times, as in 08 or during COVID.
Increasing supply does always change the supply/demand curve, and we have a massive shortage of supply in the housing market.