In geological time, these terms have specific meanings, but otherwise, according to the Wiktionary, they have similar meanings.
Eras are divided into periods, epochs and ages.
Era: several hundred million years
Epoch: tens of millions of years
Age: millions of years
For your question however, anything digital or Internet related is not going to qualify for any of these words using geological definitions, and the exact definitions of these words are much more relaxed.
"Era" is used colloquially to refer to any period of time with a name. (http://en.wikipedia.org/wiki/Era#Colloquial_.22eras.22).
It seems to be more common to call it the "Information Age", as evidenced by Wikipedia and Google search results:
Number of search results from Google:
digital age - 986 million
digital era - 309 million
digital epoch - 8 million
Internet age - 1010 million
Internet era - 126 million
Internet epoch - 7 million
information age - 1450 million