In the UK a Secretary of State is a Cabinet Minister in charge of a Government Department.
Ministers of State are junior to and responsible to their Secretaries of State. They tend not to sit in cabinet but may be members of a cabinet committee.
Of course (to muddy the waters further! LOL)
A Permanent Secretary is the civil servant in charge of a government department, who (usually) stays in office despite a change of government.
A Minister is a politician appointed by the PM,who leaves office after a change of government(or often before!).