Differences in TKD styles
For the most part, TKD is TKD is TKD. A front kick in WTF looks like a front kick in ITF looks like a front kick in ATA, etc. Differences in execution are relatively minor, even if you go from TKD to a Karate flavor, the techniques are pretty much the same. The differences between TKD and Karate are the emphases placed on various techniques. TKD in general tends to favor more leg techniques and less hands, while Karate is more towards the hands. Where the TKD flavors differ majorly is in forms and tournament sparring rules. WTF uses TaeGuk, ITF uses Palgue, ATA uses Songahm form sets, WTF sparring requires a fairly heavy hit while ATA sparring is light contact. It's not a huge difference in the tools, but in the application of said tools.
Differences between TKD and Karate
There is a chance that Karate could be included in the Olympics. Golf and Rugby are on the slate for the 2016 Rio Olympics. They changed the rules slightly, in that there are 25 "Core" sports, and room for 3 rotating sports. The rotating sports can be included or removed from the program by a simply 2/3 majority vote among IOC voting members.
After each Olympics, the IOC gets together and decides the inclusion or exclusion of sports, which is where the lobbying and confirmation of Olympic eligibility and all of that occurs. It's covered in Chapter 5 of the Olympic Charter (Last revision in 2010 or 2011, IIRC.) I think the earliest karate could be included now would be the 2020 Games.
Where I would see Karate being different from TKD, and thus meriting inclusion is if they modeled it after a NASKA event, and had such things as creative/extreme forms, breaking and weapons competitions.
As far as the differences in techniques, remember that you are seeing a limited set of techniques that are designed to score points according to the rules. (Like boxing, that uses head gear for Olympic bouts.) TKD schools do teach the other techniques, but it's hard to score points in WTF style sparring using those techniques, so you rarely see them in competition. In that sense, yes, there is a divergence. You can find WTF tournament schools that place a heavy emphasis on tournament styles, and "traditional" TKD schools that don't support tournaments much and place a different emphasis on techniques used.
One interesting rule change for Olympic TKD (In the whole anti-concussion movement in sports in general) is that head contact now only has to make contact to score a point, which is a big downgrade from the contact needed previously. I have not found whether this change is in effect for the Olympics only, or if it will be continued after the Games are over.