U.K. gov't: Minister v. Secretary of State

In popular culture, I have always heard that the British government is headed by “ministers” – prime minister, foreign minister, etc. And, indeed, in Yes, Minister, Hacker is addressed routinely as “minister.” However, I now see that very few, if any, of the cabinet ministers actually hold the title “minister” as a formal matter; they’re mostly secretaries of state.

So, is “minister” freely accepted as an informal substitute for “secretary of state”? Is it wrong to refer to the “foreign minister” or the “defense minister”? Does the public think of them as “ministers” or “secretaries” (as we do here in the United States)?

One example of the way the titles change over time is this:

From what I can recall offhand from media, and in particular BBC reporting style, the reference as an individual’s title will be to “Secretary of State for Defence, Des Browne”, but in interview he will be adressed as ‘Minister’, or in the third person as “the Defence Minister said that…”

And no, we don’t think of them as separate roles.