Well ,no wonder that is such confusion because the world it is a complicated place …(joking)
We have 2 ancient models that were combined and improved by history until The Enlightenment era.
Since The Enlightenment we only changed some aspects but not the model and nobody (except the radicals) for 200 years thinks that the model can be changed significantly.That is it ,the best political model is the liberal democracy.
The similarities are that they both are liberal democracies.The social democracy it is a branch of the liberal democracy. To be correct we should say „the liberal democracy ” and „the social liberal democracy ”.
So we have 1.the Greek Athens direct democracy,which was not quite as direct and mob rule as people think and 2.the Roman Republic which was a representative democracy but not so representative as people think.
On those 2 models the English parliamentary monarchy was build,the republics of the Italian free cities of Venice and Florence,the Polish-Lithuanian Republic of two nations .Please note that all democracies were maritime cultures,civilizations based on sea commerce and travel,where the people were physically free and then mentally and politically free.That does not mean that a seashore is enough to have democracy,just it points out that to be free one must have the freedom to choose.
With those improvements came The Enlightenment era and the first model was the USA Constitution ,the first liberal democracy that had the democratic principle of people sovereignty filtered through two check mechanisms 1.the constitutional principles and 2.the elected representatives.
Liberal democracy for all intend and purposes means an Constitution based representative democracy.
The liberalism is the first political ideology in the world and the goals were individual freedoms:freedom from monarchy,freedom from the government,freedom from the church,freedom from the economical monopoly,freedom from being harmed or oppressed by others.
Those goals are very well achieved by the liberal democracy but it is not an efficient system and it can not be successful without autonomous,responsible,freedom loving citizens.
The social democracy is a branch of the liberal democracy and it has the beginning in the French Revolution of 1789 and „The declaration of the rights of Man and the Citizen”.
The social democracy emphasize the role of the society and the citizens rights and duties.
To achieve those goals of „liberte ,egalite, fraternite”( did everyone notice the brotherhood and equality part?) the social democracy has bigger gouverments,more rules and regulations,less individual freedoms and more social benefits.
For a real practical distinction, the role of the parliament it is a definitive sign.
The social democracies tend to give the Parliament less powers and prominence ,tend to have just 1 chamber Parliament,tend to have by design less debate and opposition in the Parliament,tend to have many small parties that form great coalitions which acts like an one party state or even a real one party state.
So the distinction between the liberal democracy and the social democracy it is contained in their own name :one prioritize the individual freedoms and the other emphasize the social rights.
The risks are :for the liberal democracy to devolve, to the right ,in an oligarchical system and for the social democracy to devolve in full blown socialism.