Why does my Mac start up immediately when plugged in, while my iPhone needs to start up?
What causes the difference between my mac an my iPhone, where my Mac
  can boot and become useful immediately after being plugged in, while
  my phone needs a couple of minutes before it can even start to boot?


The primary source of power for a mobile device is it’s onboard battery. So it needs to be charged to some degree for the device to work.

When you say your Mac I am going to assume it is a MacBook of some sort. Because in the case of laptops, the system is designed to either run off of the built-in battery power or off of direct AC current if it detects it is plugged into AC power.