One might assume that anyone who's enthusiastic enough to enable Google Now On Tap, the contextual search engine that uses screenshots and optical character recognition, would also want access to Google Now cards, which depend more on location, time, and search history. But you know what they say about making assumptions. Previously Now On Tap did indeed depend on the more vanilla Google Now, or at least was linked to it, but the latest version of the Google search app for Android seems to have reduced the interdependency of these two tools.
Previously users needed to opt-in to Google Now cards on their phones or tablets in order to access Now On Tap. But with the latest server-side change, you can now disable the "show cards" option in the Now Cards section of the app's settings menu. Before now turning this off on Android 6.0+ caused Now On Tap to stop functioning - that is no longer the case. The change was first spotted by a poster over on the /r/Android subreddit.
Why would you want one without the other? Well, Now On Tap's tools are good for quickly finding information based on what's in front of you on your screen, whereas Now cards are more about your personal information and how it can be used to predict what you need to know. The latter might be a privacy concern for some users.
Image credit: Reddit user "icepac"