I think the sailors got the nickname from working with tar/pitch on the ships so much that they had the stuff/smell on them constantly....
Webster's 1913 Dictionary
n. 1. A sailor; a seaman.
1. A thick, black, viscous liquid obtained by the distillation of wood, coal, etc., and having a varied composition according to the temperature and material employed in obtaining it.Coal tar
See in the Vocabulary.
Mineral tar
(Min.) a kind of soft native bitumen.
Tar board
a strong quality of millboard made from junk and old tarred rope.
Tar water
a - A cold infusion of tar in water, used as a medicine.
- Knight.
b - The ammoniacal water of gas works.
Wood tar
tar obtained from wood. It is usually obtained by the distillation of the wood of the pine, spruce, or fir, and is used in varnishes, cements, and to render ropes, oakum, etc., impervious to water.
v. t. 1. To smear with tar, or as with tar; as, to tar ropes; to tar cloth.
[imp. & p. p. Tarred ; p. pr. & vb. n. Tarring.]
To tar and feather a person
See under Feather, v. t.