"Christian Democrats" in this sense simply mean they support democracy (as opposed to authoritarianism) and Christian social doctrine developed in 19th century Europe. When the party grouping was formed in post-WWII Geramny, it was understood that Christianity (in the European state church Protestant or Catholic varieties) had historically supported a lot of "strong men" autocrats like Bismarck or Meternich in the early modern ages when representative politics was in its infancy. The term "Democrat" simply shows they were committed to the democratic ideals.
"Christian" refers to a belief popular in European Christian social circles that the state is obligated to promote public order by looking after the needy and to promote an orderly public environment.
Looking from Asian or American Christian perspective this concept is pretty alien. Just because they call themselves "Christian" does not mean they will be like Jerry Falwell, even among the most conservative CDU people.
And in addition, as European countries go even more secularized they may be nothing but an archaic expression. It is today understood simply as the party that does not as favourable to social welfare state as the other major party (inevitably called "Socialists").
Thank you both.