Socialist - Abolishment of private property, all property belongs to the state except personal property, this may vary in some socialist nations such as Britain but general principle. Government is a primary competitor and provides all welfare and essential services, though depending on the country may also allow private competitors in these areas.
Democratic Socialist - Private Property stays private. Welfare programs are entirely managed by the government along with CRITICAL services, commonly seen as healthcare, retirement programs, etc.
Social Democrat - Government is a competitor not sole provider for Critical services and should offer them. Welfare is given by the government though private businesses may provide the service, but the service will be offered, i.e. Government pays PECO to give you electricity.
Along with the strictness of the system comes higher taxation and necessity for income redistribution and additional government oversight.
As far as ideology goes they are on the same track, they just break down more and more into the role of the government in the lives of its people and the extent that the means of production must be seized.
In general there are many types of Socialism as an ideological concept
http://www.philosophybasics.com/branch_socialism.html - includes the history of socialism with descriptions of each of the systems and conflicting views
What I describe as a Socialist is adherent to Libertarian Socialism
As for Social Democrat describes as the gradual transition from Socialism to Capitalism