During Either Player's Turn Spell Speed?

The old convention, "During either player's turn," has been updated to "(Quick Effect)". If you see either of those phrases in the activation text of any card, the effect is Spell Speed 2. Otherwise, the effect is Spell Speed 1.

Is during either player's turn a quick effect?

It's important to note that even though the text says “Once per turn,” they also say “during either player's turn.” That makes them Quick Effects, not Trigger Effects, so you must directly Chain them to the other card or effect that was activated.

Can spells be activated on opponents turn?

The only spell cards you can activate during your opponent's turn (with very few exceptions) are Quick-Play Spell Cards.