In this era, navies and water thieves are essentially the same. Most water thieves pledged allegiance to some daimyo, and only then became formal naval forces.
The Mizuno family is just like this. Originally commoners, they seized the opportunity during infighting within the Satomi family to take Odaki Castle in Kazusa (today's Ota Kichi Castle), integrated the local band of Hundred Heads water thieves (the pirate force around Hundred Heads City), and then helped the current Satomi family patriarch secure the position of Family Head. In turn, they became the Satomi family's naval unit.
Afterward, with the Satomi family's support, they further unified the water thief gangs around the Boso Peninsula, monopolized the sea area between the Boso and Izu Peninsulas, and became one of the Satomi family's pillars.