CHP: Traffic, and protection details for the governor.

Deputies: Patrol is a tiny portion of what Sheriff Departments do. Many of them have massive investigation teams, SWAT teams, search & rescue, bomb squads, dive teams, pilots, detention centers, a gang unit and more. When someone gets extradited from Mexico or turns themselves over at the boarder, they usually get passed off to the Sheriff's Department (unless it's a federal case). They're the ones protecting the court house. Basically what they do extends far outside general policing. Patrol is generally much more dangerous for deputies because their backup can be 30+ minutes away. If they get shot in a traffic stop their chances of survival are much lower than PD because backup is going to be a ways out and EMTs are going to be even further. But overall the Sheriff Departments are much more administrative. 90% of what the Sheriff's Department does is things you'll never actually see unless you are a criminal.

PD: The handle the emergencies and investigations in cities. They arrest someone within the city then drive them to the Sheriff's Department. Their focus is on keeping crime in the city low. They usually have a SWAT team, K-9s and gang unit but not much else. They experience a lot more calls but don't have to handle the detention or security side of LE.

There's also a lot of LE agencies in California that fall outside of these 3. There's the DA of each county who works a lot with other agencies and conducts their own investigations. There's CDCR who run the state prisons plus the parole. There's the probation office of each county. Then there is the State Attorney General's Office which oversees a lot of different investigative agencies who specialize in different areas. One example is the state ATF.