I doubt there's an exact definition, but to me "show" can mean that it will bring up an entirely new view (some existing UI element), whereas "surface" means it

I doubt there's an exact definition, but to me "show" can mean that it will bring up an entirely new view (some existing UI element), whereas "surface" means it will be inserted into the context already being discussed. That is, "surface" means the data is brought to you in your current context, whereas "view" means you are taking to a new context that includes the data. In this discussion, they are saying that when you search for "lyft" in on-device google search, it will incorporate Lyft info into the search results, as opposed to giving you an option to launch the Lyft app. So when they say "we will surface this data" they mean we will show it, not that we will allow the normal software to show it like normal.