In a homoplasmic individual, all mitochondria is the same. Therefor will be the same amongst cells and between siblings/mother. Unless some mutation occurs. A homoplastic individual either has all mutated mitochondria or all functional mitochondria of the same type.
A Heteroplasmic individial (more than one type of mitochondria) mitochondria occur when a mitochondria has accumulated sufficient mutations. When a hetroplasmic mother has children, the siblings have varying ratios to each other and the mother.
When you produce oocytes, a selected number of mitochondria are transferred into each. During maturation, there is a rapid replication of mt-DNA, which can lead to a random shift in mutated DNA between the offspring and the mother. This is the mitochondrial bottle neck. Bottlenecks enforce mechanisms that omit cells or individuals, in this context mitochondria, ideally such that only the healthiest mitochondria are transmitted.
In a heteroplastic individual, different cells or populations can have varying amounts of of the mutant mitochondria (including complete homoplasmy).