unlocked device vs. unlocked bootloader I've always thought that if a device is unlocked it means that it works
with different carriers. If the device bootloader is unlocked, then does
this mean the device will automatically work with different carriers?
That is do unlocked device and unlocked bootloader mean the same
thing?

All I know is that an unlocked bootloader is easier to root as commands
can be sent to the device using the fastboot protocol used to boot it
so it is not necessary to take advantage of an exploit on the device
in order to root it.

I want to know if unlocked device and unlocked bootloader are synonymous.

Thanks.
No, they're completely unrelated things. As you say, an unlocked device means it's not locked to a particular carrier: you can insert a different SIM card to change to a different carrier, and it will work. A locked device will not connect to another carrier if you change the SIM card.

The bootloader is the first thing that runs when you turn the phone on: it's responsible for loading the core Android code, so that Android can load itself and run. A locked bootloader uses digital signatures to verify the Android code it's loading, which means it will only boot a ROM (firmware image) that's signed by the device manufacturer. In contrast, an unlocked bootloader will load any ROM. Unlocking a locked bootloader will wipe all user data (but not the ROM) from the device. This is a security mechanism, so you can't get at the data on a phone by installing your own ROM on it.