Open Settings on the iPhone
Tap your name at the top
Tap iCloud
Turn off the apps and services you do not want synced
Tap Photos and turn off iCloud Photos if needed
Tap Messages and turn off Messages in iCloud if needed
Tap Contacts, Calendars, Notes, or other apps and turn off sync as needed
Open Settings
Tap your name
Tap Find My
Turn off Find My iPhone if needed
Open Settings
Tap Mail
Tap Accounts
Select the account you want to unsync
Turn off Mail, Contacts, Calendars, or Notes for that account
Open Settings
Tap General
Tap AirPlay & Handoff
Turn off Handoff if needed
Open Settings
Tap Bluetooth
Disconnect paired devices if needed
Open Settings
Tap your name
Tap iCloud
Tap Manage Account Storage if needed
Delete backups from the other iPhone if you want to stop shared backups
Sign out of the Apple ID on one iPhone if you want complete separation
Open Settings
Tap your name
Scroll down and tap Sign Out
Choose what data to keep on the device
Use a different Apple ID on each iPhone if you want them fully unsynced