secretary is either an administrative assistant in business office administration, or a certain type of mid- or high-level governmental position, such as a Secretary of State. The executive secretary (sometimes called administrative assistant or associate) has a myriad of administrative duties. Traditionally, these duties were mostly related to correspondence, such as the typing out of letters. The advent of word processing has significantly reduced the time that such duties require, with the result that many new tasks have come under the oversee of the secretary. These might include managing budgets and doing bookkeeping, maintaining websites, and making travel arrangements. Secretaries might manage all the administrative details of running a high level conference or arrange the catering for a typical lunch meeting. Often executives will ask their assistant to write original documents for review and also to collaborate with others. They may also do personnel paperwork which used to be thought of as a Human Relations function; this might also include understanding the complex rules regarding Visa and Immigration. Answer received from : https://answers.yahoo.com/question/index?qid=20080302194655AAjzHw1

I am not a native speaker, but in my opinion secretary sounds more sophisticated. It is a bit higher than just assistant. For example you use secretary in 'State Secretary', and you do not use 'State Assistant'. But basically it is more ore less the same thing.