To my limited knowledge - you must train differently depending on what you want to achieve. E.g. to lose weight one should do small weight lifting with lots of repetitions (also - according to my limited knowledge). What are the traits of other workout types (gain muscle strength, improve stamina, etc.). And what are the types of workouts in general?
If you interpret "lose weight" as "lose fat" then there's no reason you can't do all three things at once. I don't agree that there are "types" of workouts, just different goals. Someone that just wants to lose fat might just run on a treadmill, but that doesn't mean that lifting weights wouldn't be equally (or even more) effective at that goal.