There are three main factions in WotS4. They are as follows:
The Shogunage Forces (幕府 勢 bakufu zei) are the government of Japan. Read more about the the Shogunate on Wikipedia.
In WotS4, the following characters are part of the Shogunate Forces.
The police captain.
Deals with foreign affairs.
A minister who comes to straighten up Amihama.
Daughters of the minister, Kinugawa, and in charge of torturing.
The foreigners (外人 勢 gaijin zei) in WotS4 are from England. There are three primary characters.
An ambassador from England, this little girl is in charge of the Foreigners.
Some foreigner guy. Runs the casino in Amihama.
Captain in the English Navy. Laura's bodyguard.
A group within Japan which seeks a policy of complete isolationism, the anti-foreigner powers (攘夷 勢 joui zei). Read more about anti-foreign policy on wikipedia. The fictitious organization in WotS4 is called the Hannya-dou, 般若堂.
An assassin in the Hannya-dou.
Akagi is the leader of the Hannya-dou.
Akemi runs a bar in town called Truth. It is a gathering spot for the Hannya-dou.
There are dozens of characters you can find around the city. Some give you random quests. Some are somewhat main characters, such as the members of the elite four and the other four guys.
The Thief is located in the Port next to the clean nut's house. He is a member of the Elite Four and talking to him starts the Thief Quests.