IUI is the process of placing sperm into a woman's uterus when she is ovulating. This is commonly known as the "turkey baster method", and can be done at home, with the assistance of a nurse, or at a clinic. This is the cheapest option with an approximately 10-20% success rate per attempt. Each vial you store can be used for one attempt at IUI.
ICSI is typically used as part of the In Vitro Fertilisation (IVF) process. It involves the injection of a single sperm that appears healthy and motile directly into a mature egg. IVF is a more expensive option, but can be covered by your insurance provider or employer. Each vial you store can be effectively used on an unlimited basis, as it requires just one motile per attempt.