The terminologies of political ideologies are really complex to explain as well as indeed maniac for most people unless they are keen to study political science. In particular, when it comes to define Socialism, the definition varies across interpreters. Moreover, Social Democracy does not exactly imply Socialism whereas Democratic Socialism implies Socialism for certain.
The definition of Socialism involves a wide range of policy-implementations in terms of both economic and social scales. Generally, Socialism means to proactively take the external influences of policies on society (taking an account of the group of individuals, their interactions, and the external environment where they cohabit together in) into consideration. The fundamental problem of Socialism is the subjective interpretation of what are good for society so that its interpretation often depends on each interpreter implementing Socialist policies.
Focusing on the economic policies, Socialism is often used as the synonym of the collective/command economy based on the cohesive planning ahead as opposed to the market economy based on the laissez-faire planning. The market economy allows each individual economic agent to decide while trading their goods and services where it relies on the spontaneously driven distribution order. By contrast, Socialists insist on planning of, or intervention to at least, economy to induce their desired outcome. There tends to be a paternalistic institute, which can be either government or commune, instructing each individual and their firms with reference to their Socialist planning.
The types of Socialism are unique from each other depending on the instrument of implementing their policies interpret as producing good outcomes for society. Their uniqueness is more obvious in the social-policy scale than the economic-policy scale of political science. The orthodox Marxism in particular puts emphasis on the revolutionary government by the proletariat autocracy commanded by the chosen elites selected from the proletariat citizens who are supposed to be excel at knowing what are the best for their society are. Anarch-Syndicalism relies on the community of individuals who are voluntarily gathered into it from any social background to negotiate and decide their policies to implement. Democratic Socialism stands between these two policies as it allows the open political decision-making processes while it weighs on the responsibility of the chosen represents by non-random selection.
The confusion is that Democratic Socialism and Social Democracy are not technically equal to each other. Democratic Socialism prioritises the paternalistic planning/intervention into individuals' life and their living environment (i.e. society) while encouraging the minimum required open decision-making processes. Social Democracy still takes policy-impacts on society into consideration to the certain extend. However, it defies the paternalistic collective order and responsibility imposed by Socialism restricting each individual's freedom of choice and voluntary will.
In terms of the social-policy scale, the difference between Democratic Socialism and Social Democracy is slight because both support the open decision-making process conducted by the representatives elected by the citizens as well as the certain degree of political freedom for individuals unless threatening the system stability. On the other hand, in terms of the economic-policy scale, their difference is obvious. Social Democracy embraces the market economy with the optimum level of the intervention required for solving their social issues of concern whereas it avoids being the perfectionist paternalism suppressing both economic efficiency and individuals' own freedom of choice.
Social Democracy is actually the derivation of Liberalism encouraging each individual's own voluntary actions and free will instead of collectively intervening into them. Social Democracy is relatively more friendly to Socialism than the other types of Liberalism. It trusts in the invisible hand spontaneously adjusting the socioeconomic environment by letting individuals and their interactions be free. This is the critically unique point distinguishing it from Democratic Socialism supporting much stronger interventions into individuals and their interactions for their perfectionist objective.
Sum up, the word order makes a distinctive contrast between those two policies: Socialism and Social Democracy. They are neither exactly different nor same. It may be insignificant in our daily life and journalism meanwhile its difference is significant in political science. Hence, it is important to take enough attention to quote this kind of terminologies.