It isn't necessarily true that in English there is 'always' an article, for instance, "Welcome to the town meeting. Meet Roos and Willem. She is Treasurer, and he is Secretary." You may add "the" in front of the titles, but you don't have to.
You could leave out the "is" but not the "the", but it would sound accusative. "She the treasurer and he the Secretary."
This is because essentially in English we treat a job title like a title, perhaps going as far as referring to people by their title, "madam treasurer, Mr Secretary."
Not so. He is Captain.
He, the Captain, has a peg leg. He is the captain of the vessel.
One is a title and the other is a descriptor.
Misleading and completely wrong. Omitting "is" (the verb) means this is not even a sentence! An article is optional depending upon context - there must be thousands of amateur sports and hobby clubs where a keen individual is introduced to new members as "Mr A, Secretary and Treasurer of the XXX Club"
If the role is a profession, then include the indefinite article: "I am a teacher", "she is a lawyer".
If it's a role in an organisation, either leave it out or put the definite article- "he is [the] treasurer of the Football Club", "she is [the] chairman of the PTA " etc
You can omit the article in English in very specific discourse-constrained cases. For example if we're talking about roles in a formal group, "ok, who's treasurer?" "John is (treasurer). Anne's president." Etc. That's OK for me.
This will confuse you, but they are actually different jobs.. run this through google translate https://onzetaal.nl/taaladvies/advies/secretaris-secretaresse