Q: Why is social democracy discussed?
A: Because social democracy is not all welfare states, but a tradition within (democratic) socialism and it is one of the many ("democratic socialism can support either revolutionary or reformist politics as means to establish socialism"); in other words, all social democrats are democratic socialists but not all democratic socialists are social democrats. The most common name for the classification to which social-democratic parties belong to is (democratic) socialist. These parties were mostly associated with the Socialist International. Many of them self-describe as democratic socialist or social-democratic. When we use these terms to describe parties, etymologically they mean the same thing. We do not want to imply that they have two ideologies under the same roof as, for example, the Democratic Party does with Bernie Sanders, AOC and Ilhan Omar as "democratic socialists" (which is what they call themselves) or social democrats and all other major leaders as liberals. Of course, socialist parties have left–right divisions and they are sometimes called democratic socialist and social-democratic. The new party family that has emerged, which is made up of Marxist–Leninists, Trotskyists and more left-wing socialists, is now generally referred to as "left parties". In addition, when academics make a sharper distinction between the two, they are mainly referring to the Third Way development of social democracy, which saw a turn to the right that critics label neoliberalism and in practice an abandonment of even moderate social democracy.
Q: Why is the Nordic model discussed?
A: Because there exists at least three models of welfare states (conservative, liberal and social-democratic/socialist) and it is relevant as democratic socialists were pivotal in building it in at least one country. The philosophy of socialist parties such as the Swedish Social Democrats was that if people were healthy, well-educated and had a decent standard of living, that they would seek to develop a socialist society. They did not consider the welfare state to be socialism but a necessary condition for its development. However, as the Swedish Social Democrats built the most comprehensive welfare state, the welfare state is sometimes referred to as social democracy. Of course, socialism as social democrats understood it did not happen and right-wing parties in countries such as Sweden, among others, also came to support the welfare state. Nowhere is it stated that the Nordic model is socialist (the social-democratic/socialist model is not economically socialist, if by that you mean the Soviet model of economy; but socialism is not just an economic system but a political philosophy, too) and the social-democratic/socialist model is used to refer to a universal welfare state and described as favouring "a high level of decommodification and a low degree of stratification". The article does not discuss all welfare states, only those where democratic socialists have played a role.

It is not original research to discuss whether social democracy as used to describe the Nordic model developed by the Swedish Social Democrats and social democracy as used to describe the ideology of the party are the same thing. The same applies to the Soviet Union. While their system is frequently referred to as socialism, only anti-communists and Marxist–Leninists consider it to be so in reality. The issue is whether or not the economy was in the control of the Soviet working class and whether the Communist Party of the Soviet Union represented them in a democratic way. And the same applies to Bismark's State Socialism or to reference any other capitalist society as socialist.
Q: What is the difference between, say, Corbynism and Blairism? Surely the difference is that the first is socialist and the second is liberal?
A: Not so easy. The difference between Corbynites and Blairites, or the difference between the left and right wings within socialist parties, is not that the former are socialists and the latter are not, but that they have different conceptions of socialism. Admittedly, many people question whether any of them are actually socialists. Yes, those to their left accuse those to their right within the party to not be socialists; yet, those to the left of both accuse them of not being socialists but reformists.