yes definitely. And this has always been the case. Different devices? in Traditional advertising they would be radio, TV, magazine, newspaper, OOH, etc
The same applies for online advertising. Things are very different if you look at them on a tablet, smart phone, laptop. Yo unwed to take into account the social integration. Even "ads" is a term that is probably obsolete now on nowadays devices. Nobody is interested in ads anymore. Relevant information is more appropriate.
If you have an advertising camping that's mean you should have a specific concept and slogan. then you will have to make the suitable adaptations for each device you want or need to use.
for example take a look at this AD for Snickers chocolate
http://images.huffingtonpost.com/2012-06-01-snickers_sex.jpg
this is the main concept which has been displayed in Europe.
then watch the most famous and most popular TV channel in the Arab world "mbc"
you will see this AD as TVC in a same concept & even the same slogan " translated to Arabic " but just with some important adaptation on the artwork.
a modifications to be suitable enough with the Islamic and Arab mentality and behavior.
http://www.youtube.com/watch?v=PECNlwyF_EU
I think using a different ads for the same campaign especially in the same period of time that's will may broke down the camping efficiency and scatter the audience memory.
by
Ghina Said , Public Diplomacy and Media Outreach Expert , European Union Delegation to the UAE
You always have to take into account the different devices people use nowadays to view webpages, forums, ads etc. A successful campaign is one that is easy to relate to and use, one that can be viewed comfortably as well. So, you may not need to have a set of different campaigns, but a campaign that is well structured and whole.