The CTO title came into existence initially so as to have a nice-sounding title to give to technical founders who until then tried to be VPE but often failed due to lack of management experience/ability. It stuck around because it sounds nice, and nature abhors a vacuum, meaning that now that the title exists, people understandably want it.
Indeed, as others have already amply commented, what the responsibilities are for CTO varies dramatically according to what is being built. This is unlike say, a VP of Sales position in which the primary job responsibility is always the same no matter what it is that is being sold: revenue generation. A CTO may be great at giving talks or writing papers - or talking to customers - but may not have actually written code in a decade. Or a CTO can be a highly introverted top technical guy who maybe owns one tie. Both are valid archetypes. It just all depends on what the business needs.
Now if the person is expected to actually code / make shit work, you are talking about either a CTO of the coding variety or an architect/lead developer. You are not talking about a VPE because the primary skill of a real VPE is managing people and building organizations. Not unless that VPE will have both budget and time to assemble a team.
The difference between a CTO and a lead developer is what unusual and highly valuable skills they bring to the table. In my view, these skills should be technical; if they are too much on the business-side, then perhaps that equity should be going to a VPM or such instead. The old, but still very pertinent, engineering pay scales at Sun Microsystems required 'demonstrable recognition as an industry expert in a specific technical area' to move beyond a particular pay grade. Think of that as the bar for a CTO, at least for anything that is serious product development as opposed to mostly a business execution play.
A final thing to keep in mind is that while titles may be free in startups as the old adage goes, the cost of having to take a title away from someone who still has significant value to the organization is anything but. (Indeed, that's how the CTO title came about in the first place :-)