As president here is a specific use of as which means "in one's capacity as". As far as I can tell, it should be used with specific positions within an organisation, and not general occupations.
So you can't say:
- As teacher, I am giving you two weeks' detention!
But you can say:
- As headmaster/principal of this school, I am hereby implementing these new rules.
In a large company with hundreds of managers, you can't say:
- As manager, I think our employees have been very impressive this year
but you can say
- As Regional Manager for the Southwest, I think...
So far, the difference is hopefully clear. But with the, I think things become a bit fuzzier. My intuition is that you can usually substitute as the x for as x, although there may be small differences in style / pragmatics:
(The stylistic differences may also depend on the person talking. So in the first person, both of the above examples sound fine, but if it was a third person writing a news report about the headmaster, I prefer As headmaster, [he implemented these rules]...)