The way I see stuns working, and sometimes it appears weird, is that it causes the opposition to miss 1 attack. Sometimes that 1 attack would come from the existing turn or the following turn depending on who went first and who goes first the next turn.
If you are the slower dinosaur, and you are going second and you stun, the stun carries into the next turn so that the opponent doesn’t get another attack, and you get to attack twice.
If you are the slower dinosaur, and you use an instant charge attack where you suddenly go first, and stun the dinosaur, he loses his turn for this round and the stun does NOT carry into the next round as he already missed one turn. And being faster he gets to go first in the next round.
If you are the faster dinosaur for whatever reason, and you go first and stun, the stun does not carry into the next round because the slower dinosaur misses his one attack in that round.