That would be the question, wouldn't it. Unfortunately, such fundamental definitions are never simple to create, and even less simple to agree upon. A little history may help explain how we got into this parlous uncertain state, but it may not get us out of it.
The short version of the history (which all and sundry may feel free to correct in the comments) is that the Anglophone world had a terminology breakdown right from the start: what the English called "e-science" the Americans (with our customary tin ear) dubbed "cyberinfrastructure." Then the humanities reared back on their hind legs brandishing their claws like heraldic gryphons and demanded to know why they weren't included in the discussion, which led to the umbrella term "e-research" that I prefer to use.
So we have a term. Several terms, in fact. Do we have definitions for them? Well… no, not particularly, to be perfectly honest. Being a hardheaded sort, I prefer to define by praxis. What is it that e-research does? What do e-researchers do that other researchers might not?
One thing is "use grid computing to tackle otherwise intractable problems." Grid computing is the modern version of the Cray supercomputer—more computing power than you can possibly imagine. Only it's done not with one gigantic machine, but with hosts of ordinary machines yoked together by specialized software. Think about a Google server-farm, and you aren't too far wrong.
Another thing is "generate and analyze huge piles of digital data." Instrument science, all sorts of imaging, text-mining, survey data, observational data—it's all piling up. Back in the day, there wasn't much that could be done with raw (or even cooked) data other than boiling it into a graph or chart or table for a published journal article. The advent of computers has changed that irrevocably, and data show signs of becoming just as much a first-class citizen in the research polis as the journal article or the monograph.
This, of course, creates the problem of holding onto digital data—sometimes in shocking quantity—and keeping it useful and accessible. Again, our practices haven't caught up with us on this. Some disciplines have well-established lab-notebook cultures. Many don't. Almost no disciplines have established digital-data standards and practices; the quantitative social sciences are a long way in the lead thanks to enlightened research-data centers such as ICPSR, but other fields are gamely working to catch up.
"Data curation," as it is often called, is my major professional interest in the e-research firmament, so you can expect to see it discussed often here. I am partial to Melissa Cragin's definition: "the active and ongoing management of (research) data through its lifecycle of interest and usefulness to scholarship, science, and education." I hope to unpack this definition in a future post.
A last behavior thought to set e-researchers apart is computer-enabled collaboration in various forms, from the breaking-down of institutional barriers to the spread of inter- and multi-disciplinary research teams. Social networking is often mentioned in this context, though sometimes with a bit of a sneer. Even the humanities, where scholars tend to self-define as solitary and esoteric, are beginning to find that the life of the mind can be usefully shared.
Does what I've said accord with your impression of e-research? Comments are open!