IUI (intrauterine insemination) is the simplest of all fertility treatments, while ICSI is way more complex, as it is a more direct approach at egg fertilization.
With IUI, the sperm is placed inside the uterine cavity and allowed to move forward by themselves toward the oocyte. Broadly speaking, they penetrate it under their own "power".
Conversely, with ICSI there is no need for the sperms to travel through the vaginal cavity by themselves, as a spermatozoon is injected directly into the oocyte, which causes fertilization to occur artificially.
Another difference is that ICSI occurs outside the female body, after egg retrieval. In the case of IUI, the process of fertilization and egg insemination occurs as it would occur naturally inside the woman's reproductive system.