It is not an issue, it's the expected behavior.
The thing is that the smart publish won't publish anything if there isn't any change since the last publish you did.
The republish however will publish every single item on the master no matter what.
That's why you can see the elements being (re)created on the web index when republishing but can't see anything happening when smart publishing.
You can find more information about the different way of publishing something in Sitecore on this SSE post: What is the difference between republish, smart publish and incremental publishes?.
web
database?