You mention you've been trying aperture priority and shutter priority but don't see much difference between the two. It could be that the settings result in the same exposure. For example, let's say you set your camera for aperture-priority exposure mode and you set your aperture for ƒ/11. You compose your shot, and the light meter built into the camera reads the light in the scene and determines that 1?125 sec. is its choice for shutter speed. When you press the shutter release, you capture an image with exposure of ƒ/11 at 1?125.
Now, you flip your camera to shutter priority, set the camera for 1?125 sec. and compose the same shot. The camera sees the same light coming into the camera and chooses an aperture of, you guessed it, ƒ/11. I guarantee that if you press the shutter release and take the picture, it will look the same as the first image. It's the same exposure.
But let's take a look at another exposure example—you can compare the two exposures displayed in the images at the top of this column. I recently was in Rochester, N.Y., and saw this fountain in the Maplewood Rose Garden. I found it a perfect opportunity to shoot examples of different exposure-mode settings.
The image on the left was shot using aperture-priority mode—Av. I set my lens to get maximum depth of field (smallest aperture) so I could capture a scene showing that the fountain was in a rose garden. I used ƒ/32, and the camera picked 1?5 sec. shutter speed. With the increased depth of field, the garden comes into focus, but the fast-flowing water becomes a blur.
Next, I shot using shutter priority—Tv, as shown in the image on the right. I wanted to freeze the water and make the background subtler. I chose a shutter speed of 1?2000 sec., and the camera picked an aperture of ƒ/2.8. The fast shutter speed was more than enough to freeze some of the droplets in midair. Of course, the depth of field was as narrow as I could get it with the lens I was using, so the background is unrecognizable.
This is an extreme example, but it's something you can prove to yourself with your own camera. In this scene, a tripod is a must because of the slow shutter speed, but you could try other scenes without a tripod. For example, photograph athletic events or street scenes. There's usually fast movement that you can capture. See how choosing between aperture or shutter priority can change the feel of the image. Just pay attention to the shutter speed and aperture settings. Make sure that you don't end up with the same exposure settings for both exposure modes.
After seeing the example images and reading about the explanation of aperture versus shutter priority, it's easy to fall into the trap of thinking that if you want to control shutter speed and its effect on the image, you should always have the camera in shutter priority. That isn't always the case. Although somewhat counterintuitive, if you're in a situation like a sporting event and you want to freeze the action as much as possible, aperture priority may be your best setting!
Why? If you use shutter priority, you might limit the maximum shutter speed you can use. You might set your camera for 1?125 sec. and find that the camera is choosing ƒ/4, but the lens you're using could go down to ƒ/2.8. At the very least, you'll spend a lot of time fiddling with the shutter-speed setting. Instead, use aperture priority and set your camera for the largest aperture the lens provides—in this case ƒ/2.8. The camera will then select the fastest shutter speed possible.
Try it yourself and you'll see that even aperture priority can make the shutter a priority.