Is Mixed Economy in Economics the same thing as Mixed Economy of Welfare in Social Science ?

Economics is not politics, but it is so intimately connected that you are not likely to hear anything that makes sense.

Did you buy something today? Let's suppose you bought a pencil. so you cast a vote with your money for one pencil and passed up all the others. Which one did you vote for? Was it a certain color? In a certain store? Or did you just grab something from a display near the checkout line? The sum of all such decisions in a certain area make up the economy for that area.

Politicians desperately need people to think they are making things good, so they distort economic reports to minimize bad news and maximize good news, even if they have to lie. That is why you hear politicians claim to have reduced the deficit when clearly the deficit is still rising. In reality, they only reduced the rate of increase.

So when you hear things like "mixed" economy, you can look for the supposed mixing to see if reality is being described. Politicians and bankers still use Keynesian economic theories, even though they have been thoroughly discredited. Keynesian theories use the same words as traditional theories, but they turn the charts sideways because that seems to justify tax-and-spend policies. Keynesian theories emphasize the money, rather than the decisions. You can learn theories based on reality at mises.org