Do all of the following carry the same semantic meaning? If not please explain your answer.
1.
OK, this is a good question, and in short this is what happens when two or more specs proposing similar problems get released at different times and supported by different browsers/screen readers.
The element should be given the navigation role automatically, so in theory you can just use your option 1. However, some screen readers don't know that yet, so using 2 would be better. Option 3 seems odd, as it's more than a unordered list, it's a nav.
Of course, this is a nice example – for many ARIA roles, there isn't a HTML element to match, so you might go for option 2 because you are using other things from ARIA, and want to be explicit.
Personally, I use 2 because GZIP makes the file size irrelevant, and it makes it work in the AT I tested with (Voiceover and something else on Windows, I can't recall right now).