A Drayman was historically the driver of a dray, a low, flat-bed wagon without sides, that was used for delivery of all kinds of goods. Now the term is really only used for brewery delivery men, even though routine horse-drawn deliveries are almost entirely extinct. Some breweries do still maintain teams of horses and a dray, but these are used only for special occasions such as festivals or opening new premises.
Also note the word "Drayman" is heavily referenced in US Ports as the over the road highway truck driver who delivers containers to and from the port.
A drayage company and draymen provide carriage from or to a port or rail ramp. The items hauled are either ocean or rail containers. The contents are either cross docked for outbound long haul carriage or the container is drayed to the receiver who unloads it. The drayman then hauls the empty back to the ocean port or rail yard.