Not all. Jailbreaking requires exploiting a (variable number of) holes in the system, while carrier unlocking requires exploiting the baseband. The former is a prerequisite of the latter, but the carrier unlock is not always possible even if you're jailbroken as it depends on holes found in the baseband, which depend on the baseband version.
I don't know about rooted Androids, but jailbroken iPhones can be unlocked.