The surname Dunn and Dunne, are they the same, if 2 people who didnt know each other both had either one of ..

Yes, as you stated "Dunn and Dunne are the same name with just a variance in the spelling. If you look long and hard enough you will find that two people with the same name have a common set of grand parents in a generation in the past. I mean perhaps many "Greats" in front of Grand Parents but if you go back far enough you will find the information. As you search back further and further you will be searching a smaller and smaller population so it gets more likely that you will locate the information in the next earlier generation.