Basically a cabbie in new york, according to regulations, HAS to stop for anybody that hails them.
That has to mean if the taxi is free, so that you can't discriminate people, like "That dude looks like a hobo, so I'm ignoring him, I'm looking for someone who looks rich.".
You can also "call a cab", then a taxi driver somewhere hopefully nearby will put on his meter and come to pick you up. Surely he doesn't have to stop for anybody hailing. (Otherwise it would be more like call and pray taxi service).
There's no difference between calling and mobile-app-hailing, except the way the order comes through.
The central depends on people calling taxis to make money. They don't like people being able to bypass them.