Liberalism could be said to revolve around freedom from the power of the mighty, and Socialism around freedom from the power of the rich. Democratic freedom is per definition a Liberal virtue. Some Social democrats might be classified as much of a Liberal, but most are definitely not. The program of the Social Democratic parties are not understood as Liberal, but when it comes to practical pragmatic politics and policies the outcome might be a mixture between the own program and other ideas. Conservatism is likewise defined as ideas succeeding the writings of Burke, Disraeli and other classical political writers.
Socialism is the people's control over the means of production.
High spending government is something different. As an ideology, Socialism deals more with the political basis than with the implementation. Nobody can justify taxation as a goal, that politicians and civil servants are always right, that it is a goal to confiscate any kind of private property. There are some Socialist ideologies that want society to build upon omnipotence. All but tiny extremist groups have survived.