With the caveat that specific organizations may differ in how they use these positions, it is my experience that in most organizations, the basic differences are 1) the degree of decision-making authority, and 2) the sophistication of tasks that might be assigned to the individual. An example may help illustrate.
A secretary will in all likelihood be assigned strictly clerical tasks, e.g., typing, filing, copying, dictation (a quaint "old world" practice that is not much in use any more), and possibly some simple scheduling tasks, but will have little or no authority to act or make decisions independently.
In contrast, an administrative (sometimes called an "executive") assistant may, for example, be given decision-making authority to resolve complex and conflicting schedule demands using independent judgment, knowledge of the importance of the individuals wishing to meet with the "boss," the nature of the business, other competing time demands, and the boss's personal preferences.
An administrative assistant may, for example, also be given responsibility for designing and completing longer-term projects of interest to the boss, such as surveying key customers on a specific issue or product, but which are not critical to the organization's business plan and where the results don't have to be statistically validated.
It is extremely unlikely that a secretary would be assigned such tasks, except perhaps to assist the AA with tabulating results or typing of the report.
Is that helpful?
32+ years in executive positions having secretarial and Administrative/Executive Assistant support.