What does definitively mean?
Definitively is a stronger word — anything definitive is official or conclusive. If a doctor gives you a definitive diagnosis, you know exactly what’s wrong. It’s not a promise that something will happen; it’s a done deal.
Which pronunciation of either is correct?
Using English phonetics, [ EE-ther ] and [ AHY-ther ] are both correct. As a side note, giving “th” a phonetic Z (or S or F or D) sound is a common mispronunciation that can be corrected with practice.