Beverly Hills, Santa Monica, Culver City, Torrance, West Hollywood, El Segundo for example are all Cities that are surrounded by City of L.A. but within LA county
The way these Cities within LA County provide basic infrastructure services can very greatly. Some have there own Police and Fire. Most have various level of Public Works (permitting, street lights, engineering, etc). Some the County provides more.
Pasadena, Glendale and Burbank even have their own electric companies for instance.
Alta Dena I think hasp a lot of LA County services.
LA county when it comes to basic service infrastructure is smaller in size that LA City and more spread out. Cause LA has the majority population and some large cities within LA County do a lot of stuff themselves.