Haha good question.
Both terms are meant to make a clueless person sound smart. I'm kidding, sort of.
It depends on the person, industry, firm, sector, whatever. They're vague terms.
"Strategic management" is not really a "job" but more a responsibility within a job. For example, it's a big part of what a CEO or high up exec will deal with - long-term planning decisions about where the company should be headed in 5-15 years in terms of product mix, operational efficiency, organizational hierarchy, development of key managers, regional/international expansion, and how to grow (through acquisition, organic growth, JVs, etc.). Of course for many publicly traded companies this function ends up becoming more smoke and mirrors, since the executive team is being judged by Wall Street based on quarterly (and maybe annual) performance. So even as an area of responsibility, "strategic management" is really not as important as it sounds (or as important in practice as it may be in theory). Everyone is focused on quarterly results.
"General management" is a catch all term for someone who doesn't have a specific job function, but is responsible for a company's product or region. Of course if it was a one-product company with only one office, then the only true "general manager" is the CEO. Medium- to large companies usually have multiple product categories and multiple regional presences around the world, so the "general manager" function would be the folks who have profit/loss responsibility for a product or region (i.e. they are the "mini-CEO" of one line of sales). In consumer products such as P&G, Unilever, etc. this is usually held by the brand managers. In most other product-oriented industries, they are usually called the product managers.
Hope this helps -- if you're not clear about it, don't worry because it's not really supposed to be clear. Corporate language like this was designed to be deliberately ambiguous. The word "strategic" is the ultimate word used to make anyone sound smarter or more knowledgeable than they are in any workplace. Try it - until some cynical person calls you on your BS haha
Alex Chu
alex@mbaapply.com
www.mbaapply.com
http://mbaapply.blogspot.com