Looking at the volume of web searches (Google data) for the two words, there a number of interesting things to note:
The glaring conclusion is that “Hellas” (the proper name for the region) is hardly used. Also “Greeks” are seldom requested as people. There is a seasonality. Searches drop off in July and August, possibly as many expatriot Greeks return to the homeland and stop searching for it online. (A smaller, similar drop occurs in December.) The most interesting thing to note about this (randomized) data from Google is that the two words do not actually always follow each other closely in their trends. It starts making sense if we see
In fact there are great regional variations to the search. In the US for example “Greek” is closely associated to Greek ancient history and Greek products. (And thanks to New Yorkers especially – obviously more concerned with the quality of their food!)
Notice the difference in seasonality as the blue line (searches for “Greece”) is relatively stable. In the UK, the picture is almost the exact opposite!