My undergraduate degree is in geography and I have been involved with GIS for over 10 years now. Therefore, I am one of the geographers who knows how to program. As a student, I was lucky enough to find an internship with a GIS consulting company that allowed me to learn all the aspects of the profession including some exposure to programming. At the time, it meant learning AML for ArcInfo workstation and Avenue for ArcView 3.x. I quickly became aware of how powerful programming could be in the GIS environment. And luckily for me, I seemed to pick it up relatively easily. Back then, however, most GIS programmers had a geography/GIS background. People in IT fields did not really know, or care to know, about GIS software and the programming languages associated with it. As newer generations of software have incorporated more mainstream programming languages and Web-based GIS development has grown, it has become increasingly difficult for individuals to know all the programming languages as well as the fundamentals of geographic information science.
It is not uncommon to see job descriptions that require knowledge of ASP.NET, C++, ColdFusion, Java, JavaScript, JSP, PHP, Python, SQL, SOAP, Visual Basic and XML from someone with a "strong" GIS background. The people who meet those criteria are probably few and far between. Not to mention very expensive! Those of us with the geography/GIS background know the fundamentals of GIS, but may not know everything about computer science. On the other hand, IT analysts/programmers have a greater understanding of computer science without knowing all the ins and outs of GIS. Mind you, neither field is so difficult that someone from one background cannot learn many aspects of the other field. It is difficult, however, to know all the aspects of both fields.
Just as in academia, where many inter-disciplinary studies have arisen that fall in between distinctly different disciplines, GIS programming will always be juxtaposed somewhere between geography and computer science. Geographers will have the knowledge of sound geographic principles and spatial analytical techniques and the work involved will be figuring out how to program to achieve the desire results. IT professionals have the thorough knowledge of programming or Web development and the work involved will be figuring out which geographic principles and spatial analyses will be required to achieve the desired results. It is important, therefore, that employers recognize where they need to place an emphasis for the services they require. Although employers may want someone who can do it all, they will have to realize that everyone will bring their own strengths as well as some limitations to the position based on their background.
As for what titles to give each group, I should probably leave that up to someone else. The best I could come up with was GeoProgrammers and ITGISers - neither of which has much of a ring to it.