Whilst I suppose a distinction could be drawn between startup and boot (boot = grup, startup = everything later), I don't think there is any difference in the way they are being used.
I prefer the term startup, but boot has more uses currently.
I suppose you will get various answers here, BUT imo there are at least 5 categories.
BIOS - update bios, set bios to boot from CD / Flash
Grub - Second step in the boot process, main issues are configuring grub.
Boot - Generally this refers to upstart, mounting the file system(s) and starting networking and services (root owned processes or daemons).
GDM / LightDM - Graphical log in screen and configuration.
Startup - Generally, IMO, this refers to a users graphical session. What programs start automatically (pulse audio, customize what applications start on login , vino (VNC), seahorse, etc) (user owned processes).