Skill Points are awarded on attainment of a new level. Swashbuckling Skill Points can be used to train Skills at any city's specific Trainer for each player's particular Avatar Combat School. You can select from: Brawling, Dirty Fighting, Fencing or Florentine.
Career Skill Points can be used to train Skills. Only in Ports controlled by your Nation you can learn those skills. A Spanish player, for example, can't learn any skills in non-Spanish ports.
National Careers:
Pirate Careers:
This information is provided by the update that PotBS Wikia is undergoing, by Captain Vuur.