A Van Driver, aka van man; drives a horse-drawn van used for collection and delivery of small goods; duties as for carman; sometimes specifically designated. e.g. delivery van driver, mail van driver, parcels van driver. "A Dictionary of Occupational Terms"
The term carter, as well as haulier, carman, carrier, can all refer to people in charge of horse drawn vehicles, a person engaged in the road transport of goods, either on his/her own account or for an employer.
There is also Drayman, Wherry Man, Van Man, Lurry or Lorry Man, Teamster, all who were people in charge of horse drawn vehicles, for the transport of goods.
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