Right, yes, same thing. One master password per account, stored locally on trusted machines (or possibly just a hash stored locally).
I went and took a look at the LastPass security whitepaper:
My reading of this, specifically of the section labeled “New Device Verification”, indicates to me that LastPass does not use the secret key architecture of 1Password, and that adding a new device requires only control over an email address, a much lower bar than that established by 1Password, where adding a device requires access to the secret key, obtained via access to an existing device with that secret key stored on it. Specifically, it appears to me that it should not be possible to gain acess to a 1Password account using only email address, master password, and ability to intercept email sent to an address.
Please correct me if I’m mistaken!