Let's fix a scheme $S$ and consider some Grothendieck topology $\tau\in\{Zariski,\acute{e}tale,fppf\}$ on the category of schemes over $S$. Define a $\tau$ fiber bundle with fiber type $F$ to be a map $f:X\to Y$ of schemes over $S$ that $\tau$-locally on $Y$ looks like a product with $F$.

Given $\tau,\tau'\in\{Zariski,\acute{e}tale,fppf\}$ with $\tau'$ coarser than $\tau$, are there conditions on $F$ that imply that every $\tau$ fiber bundle with fiber type $F$ is also a $\tau'$ fiber bundle?

I've seen examples of etale fiber bundles that aren't Zariski bundles, but it's my understanding that for $F=\mathbb{P}^1$ this can't happen (I'm not positive about this), and I'm wondering about other $F$'s. I don't know if there are fppf fiber bundles that aren't etale bundles, and if there are I'd love to see an example.