I don't understand the difference either other than Assistant seems to be replacing Now. The issue, I'm finding, is that Google Assistant requires that you turn on the recording of usage data and history to your account, such as Web & App activity, Location History, Voice & Audio activity. All recorded and tied to your account. I don't believe this was the case with Google Now.
Google, to their credit, normally allows you to erase all this data and turn recording off, but with Google Assistant, they require it all to be on and recording. I avoid using it because of this restriction.
Google, to their credit, normally allows you to erase all this data and turn recording off, but with Google Assistant, they require it all to be on and recording. I avoid using it because of this restriction.