I admire your desire to learn about various economic systems and share your interpretations. Digging through misinformation and conflicting viewpoints is not an easy feat.
I understand social democracy as equal representation, guaranteed basic needs, governance for the people, and a socioeconomic system that provides for everyone. The US intended to be a social democracy, but centralized wealth, centralized power.
Democratic socialism encompasses the same principles, but the profits from oil and gas companies (for example) wouldn't be bonuses for shareholders. The money would be reinvested in the public.
Socialism and capitalism can coexist, and for some markets, capitalism is the best option, but private companies can't efficiently provide public goods. Businesses shouldn't have to do the government's job - provide for the people, and economic policies should benefit as many people as possible.
Our government subsidizes businesses using public funds, we buy the product, and the company keeps all profits. Essentially, we have socialism, but it's not for the public.
Thanks for sharing!