I am slightly confused about how torsion behaves with base change of group schemes.
These notes (https://www.math.uni-bonn.de/ag/alggeom/veranstaltungen/Vorlesungen/2015ws_vl_morrow/2015ws_vl_p-div%20final.pdf, remark 6.1) seem to imply that torsion commutes with base change.
However, this blog post (https://simpletonsymposium.wordpress.com/2013/08/09/p-divisible-groups/?fbclid=IwAR20ydyqu1uCbfDY-3Cu83ThWSrGTjFfYFddc4Kdrhg7nEaNsNhbpq1MFas) suggest with the example at the end that this is not always the case, since we don't always have
$$ R[[x]]/[p](x) \otimes_R K \cong K[[x]] /[p](x)$$
and the LHS is just the $p$-torsors of the group scheme whereas the right hand side are the $p$-torsors of the group scheme after changing base.
Are they both right and I am misinterpreting something?