There is both a guardian of the person and guardian of the estate. The former is actual care and control of your minor children and the other is financial control. Often people choose the same person for the jobs. However, in some cases people separate it out; for example after divorce!
The key is naming guardians in your will so that there won’t be a mess or a fight after your death. The California probate code allows the Judge to make the decision that is in the best interest of the child. However, it will be presumed that you know what’s in their best interest so NAME YOUR GUARDIANS!