What are the differences between a “gaming” computer and a “working” computer?

I'm looking at buying a new laptop at somepoint and I don't know if it is necessary for me to get a gaming computer to be able to enjoy games like Fate, WOW, and Sims 3. If I don't get a gaming computer, will my normal computer be able to handle games like these? What will be the quality differences in game performance? Conversely, if I do get a gaming computer, how will that be different as far as work is concerned? Will there be any notable differences in computer performance when it comes to working tasks?
Thanks!
