Difference between "work at the table" and "work the table"

Question

According to the Human Rights Campaign website, National Coming Out Day has been held every year for 30 years on the anniversary of the second March on Washington for Lesbian and Gay Rights Oct. 11, 1987. HERO adviser Brittany Stegeman helped work the table Tuesday, which displays a pride flag and offers an opportunity for students to write encouraging notes to those questioning or considering coming out.

Source, “Northwest celebrates National Coming Out Day” by Samantha Collison

I think “work” here as a transitive verb means the following:

c [+ object] : to do work in, on, or at (an area, event, etc.)

She works the Northeast region of the state selling insurance.

Merriam Webster

However, “work” can also be an intransitive verb. What is the difference between “work the table” and “work at the table”? Are they interchangeable here?

Answer 1

The difference is that "worked the table" means that "being at the table" was the work, but "worked at the table" means that "you did some other kind of work while at the table".

In this case "the table" is a special table set up with flags and books. And the job is to be at the table and represent HERO. Because the job is "being at the table" you can say "worked the table" instead of the much more common "worked at...".

If the job was (for example) making socks, you could say "she worked at the table (while her sister worked on the floor)"

Compare this with "worked the room" — said when a politician (or similar) goes round all the people in the room, talking with each one and trying to get their support. It has a specific meaning, quite different from "worked in the room".