It seems to me that maybe the Minister definition comes from the sample, "secretary of state." During my time in Spain, I have noticed that that kind of office is a minister, i.e. "minister of justice." I think, though, that if you are just talking about "un secretario", then it should just be translated to "secretary."
I noticed that in the one sentence I encountered before, 'secretaria' - with an A ending - was used (Tú eres mi secretaria.) This stand alone noun, 'El secretario' ends in O. Perhaps that is the distinction between a hard working real secretary and the politician known as a minister. I don't know, I'm guessing.