Here's a definition from wikianswers, but I am not sure of its reliability. It seems to mesh with what I had posted earlier.
After I posted my own description/definition, it dawned on me that maybe Rick Smith has management of only football operations, not the marketing side of things and other non-football tasks. The quote below describes differences from team-to-team as to what roles their GM does and does not perform.
Exact responsibilities vary from team to team, but a general manager (GM) is usually responsible for the whole operation. Many teams however do not give their general manager responsibilities over financial and commercial operations, but rather only over football matters (including salaries of players and other employees connected to the sports operation). Some teams call this GM without financial responsibilities a Vice President of Football Operations or Vice President of Player Personnel. But the media will often informally refer to such positions as the 'General Manager' to indicate that this is the person ultimately responsible for building the football program.
The General Manager will have ultimate authority over the players, coaches, scouts, trainers, and basically anyone who can conceivably have an impact on the product the team puts on the field. Despite having hiring/firing power over the Head Coach, most GMs are expected to treat the coach as a near equal. The GM will consult closely with the Head Coach when selecting players, and it is universally expected that the Head Coach will have substantial powers delegated to him including total control of his roster once the offseason acquisitions are made, and control over his staff.
Read more: http://wiki.answers.com/Q/What_does_...#ixzz1nbzskqRJ
I think each franchise probably has its own "culture" of how it allows the GM to operate. You're probably going to find that each NFL franchise has a GM that can do sets of tasks that other GMs on other teams might not do. Think about it: When you've gone from one job to another, although the business has certain managers and certain department heads that are consistent with other businesses...not each business or entity is going to be a carbon copy of the others. What one manager can do in his current job does not mean he could become a manager at a new place of business and retain ALL of his previous roles and responsibilities...each culture will be different in many ways.