Strong Uniform Total Order vs Weak Uniform Total Order
Consider for example two processes $p_1$ and $p_2$, with $p_1$ that delivers in this order $m$ and then $m'$.
In SUTO, $p_2$ will either deliver $m-m'$ as $p_1$ did, or it won't deliver $m'$ at all.
But why?
Because if $p_2$ will deliver, for example, $m - m'' - m'$, then every process can deliver $m'$ only after $m''$.
This means that once $p_1$ and $p_2$ don't deliver the same messages, the  following  messages delivered by $p_1$ and $p_2$ must be disjoint.
In WUTO instead it's possible to have $p_1$ that delivers $m - m'$ and $p_2$ that delivers $m - m'' - m'$.
This example is taken from Baldoni, Cimmino and Marchetti, A classification of total order specifications and its application to fixed sequencer-based implementations.