My understanding is that Fill or Kill doesn't require a single fill, merely that the entire volume is instantaneously filled. So, if I send FoK Buy 100 shares

My understanding is that Fill or Kill doesn't require a single fill, merely that the entire volume is instantaneously filled. So, if I send FoK Buy 100 shares @ 500$, then I could end up with 100 fills of size 1, or 1 fill of size 100. It makes no difference (except occasionally in commissions/costs depending on exchange). However if there were only 99 shares it would not partially fill, and would simply cancel unfilled. Immediate or Cancel would allow you to get "up to 100 shares at a price of 500" and cancel instantly once available volume was consumed.