Android users who don't have root are still in jail, because even if they can run arbitrary application software, they can't choose not to run arbitrary preinstalled software, so jailbreaking is still necessary.
Since an iPhone jailbreak provides full access and is, in fact, usually used for tweaks and other modifications rather than custom apps, that is disingenuous.
An iPhone "jailbreak" both jailbreaks and roots the device. Android phones (except for very cheap ones from certain carriers I think?) only need to be rooted.
It's not disingenuous, just (perhaps overly) pedantic.
"Jailbreak" is a made up term. As far as I know, it originally referred to accessing arbitrary files on the filesystem (getting out of a chroot jail), but it now refers to a process including gaining access to the bootloader and/or kernel. Either would be an acceptable use of "jailbreak" (though the former might be misleading), but the term has never meant "run unsigned apps". HTH :p
Hmm, my impression was that the process of "jailbreaking" an iPhone was somehow rather related to breaking out of a chroot jail. I don't know where I got that impression though.
What you mean is getting root access to the linux system that android is based on. Which is a cool hack, but not similar to a jail brake.