Is there a distinction between NEOs and near-Earth asteroids? Is there a difference? My "real question" is in Space Exploration Meta (neo (near-earth-object) and near-earth-asteroid tags, do we need both?), but I think that astronomers will be able to help understand the situation and terminology.

Question: Is there a distinction between NEOs and near-Earth asteroids? Is there a difference? Or is it a distinction without a difference?

I noticed for example that here in Astronomy SE there is just near-earth-object.
Yes, Near Earth Objects (NEOs) include asteroids (Near Earth Asteroids (NEAs)) and a few percent of comets (Near Earth Comets (NECs)). As shown by the Update to Determine the Feasibility of Enhancing the Search and Characterization of NEOs (NEO SDT Report) in Section 2.3, the risk from Near Earth Comets is about 1% that of asteroids. So "NEO" tends to be assumed to mean "asteroid" unless otherwise stated.