Consulate general is the office of a consul general. Just like you wouldn’t say about someone that he’s a law office you cannot call a person in the consular service a “consulate.”
A consul general is the head of post, which is the consulate general. He may be the only consular official in that physical facility (as is often the case with an honorary position) or there may be other consuls and vice-consuls working at the same office (as with large career posts).
Here’s a good way of remembering the above: Just as you might refer to a person as “Attorney Jones” you’d say “Consul General Jones.”
Keep those questions coming; – by email or otherwise.