^^ +1 to what Dao said.
f4, ISO 100, 1/200sec in aperture priority mode, shutter priority mode, full auto mode and full manual mode will produce exactly the same image. However to get to those setting very different things happen in each mode and that is where the strength of each mode is.
Auto/program - gives you the cameras best guess at the scene and often as not can be a decent exposure; you might not get the creative control over the shot, but you normally get a pretty decent exposure captured. In good lighting its fine, in dimmer or poorer lighting (without flash support) or in a set condition like shooting the moon however it can fail.
aperture/shutter priority: These work like manual mode, but instead of you having to set all 3 settings you only set 2, whilst the camera sets the 3rd. The power of this mode is that the camera is lightning fast at changing that one setting according to the meter reading. Often in manual mode you will set the ISO, set your key setting (the creative setting you need to have control over) and then adjust the final setting till the meter reading is good. These two priority modes just do that last stage for you and in changing lighting conditions its far superior to doing it yourself
Should the camera meter be failing or you want to push the shot a little bit one way or the other you even have exposure compensation to over or under expose the shot a little.
Manual mode: Here you have full control, the camera meter still works and tells you what the shot will be exposed like, but you have the control. This is key in something like working with flash as the dominant lighting because the cameras meter will only meter ambient lighting, it has no idea how the flash will affect the scene and so pays little attention to it.
For example in a dark room the camera will still want a wide open aperture, high ISO and slow shutter speed even if you have enough flash light for a better exposure. Fighting it in the auto and semi auto modes is a waste of time - so shift into manual and you can set the settings and let the flash deal with the rest.
Essentialy spend time learning about the other modes - experiment and understand where the strengths of each mode are for yourself. After that you can pick the best mode possible to shoot with at any given time and situation.
Also remember - semi auto modes like aperture and shutter priority are things that the "PROS" asked for in cameras and they are quite possibly more popular in overall use than full manual when used outside of a fully controled studio