Both are a lot more polished as far as the visuals are concerned, with both the characters (
original vs
sequel) and the ships
looking far better than before. The weather effects also got some improvements.
Both of the sequels are set in the carribean instead of the fictional archipelago of the first game but the story (or some of the stories) are a continuation of the first sea dogs). The strange part is that despite the real setting and total absence of them in the original there are now magic/mythic creatures in the game. It's not everywhere nor really apparent but it's there and it feels off when/if you meet a magical element.
Minor spoiler about magic (how do I put a spoiler within a spoiler ??)This is probably an influence from their previous game which was based on the Pirates of the Carribean films and was supposed to be the initial sequel to sea dogs before they got the right for the franchise iirc. There were rumors about the existance of the Black Pearl ingame and there are definitely skelletons on some caves that you can explore for treasure.
Back to the more important parts.
Gameplay!
There is now a random quest generator system were, outside of the normal story quests, random npcs can ask you to do some chores (get x amount of slaves, transport x amount of some goods on y island, take said npc to x island these type of things). It's not really intersting but better than nothing I guess. I don't remember in which of the sequels it was but you could get a loan and then they would send privateers to hunt you down if you didn't pay it off.
Sailing around has changed a LOT. In the original you had a map of the area and you just clicked where you wanted to go. Some (arbitrary or tied to the wind somehow... I never found out) amount of time/days would pass and you would either eventualy go there in a straight line or stop midway for an encounter which you could sometimes avoid. In the sequels that system was ditched in favor of one like in sid meier's pirates where you control you ship and sail around the sea. Wind direction was a MAJOR factor on speed and it could also cause you to fail some quests ( I remember I often had to travel against the wind). Overall the sailling around part was quite a chore for me. To be clear the original system wasn't flawless and I lost some games due to failing to pay wages due to it but at least it was faster and you didn't spent your time just watching your ship trying to crawl around.
Combat also had it's share of changes. Ship vs ship combat was largely the same but boarding had changed a lot. Where in the original your captain would just duel the enemy captain (a'la guess what... sid meier's pirates) you now had actual crew members on each side fighting on the decks and you would have to fight past them to reach the enemy captain. Pistols/gunpowder weapons were also available and were an active part of the fight. It was somewhat more realistic and it really limited your ability to board larger ships with more crew regardless of how you skilled you were as a player but they did fix the horrible charcter controls of the original so it was ok.
The rpg elements also got more prevalent with your character (and officer's I think) having a personal inventory, customizable equipment (weapons, guns) and a variety of perks that suplemented your/their more general skills.
And now the bugs. I didn't play the sequels long enough to encounter the most troublesome of those but at least one of the main stories (the one with the kids of the original's protagonist iirc) was bugged and you couldn't progress after some point. I also had many CTDs but that might have also been my crappy laptop.