What are the differences caused by cold booting vs restarting

Are there differences in the state of a computer if it had been started from a powered off state versus restarted? The only technical difference that I know of between a poweroff then star vs a restart is that some steps in the boot sequence (mainly POST for powersupply) is skipped, but are there other differences like temporary files? Could this affect the network, for example assignment of IP addresses? Does it matter if it's a virtual machine and the host is left on?