Different camera brands and models may have different focus area options, so check yours to see what is available to you.
For most, however, they will have a wide AF-Area, a Centre AF, and a Single Point or Spot. Everything else is usually just variations on size or which part of the sensor the camera will look for something to focus on (right hand side, left hand side, etc). The terminology may be different, but the outcome is usually the same.
Mostly, I use the “Single Point” or “Flexible Spot: Small”.
This is one single AF point which I can move around the screen with the little joystick on the back of my camera. I can also touch the screen to place the point (very helpful if I’ve managed to lose it!). Different cameras will have different ways of moving this point around, but the idea is to move it until it’s over the dog’s eye. You don’t have to keep it centred! You can move it here or there, up or down, giving you options for how you want to compose your photo.
Some cameras will have more or less focus points available across the frame, it really depends. I know of some cameras which only have 11 focus points, so you have 11 options of where to move that single point, and you’ll have to compose your photo within that limitation. Other cameras have hundreds! This isn’t a reason to rush out and buy a new camera, but you will want to be aware of potential limitations if you’re trying to have your dog toward the edge of the photo and you’re unable to move your focus point there.
Expanded Single Point
This acts much the same as the single point above, however if it doesn’t manage to find a thing to focus on in the main area, it will grab onto something either just above or below, or slightly to either side of the point. I use this occasionally for action photos, if the dog is zigzagging or not running around in a predictable way (puppies!!) as it gives me just a little more opportunity to get focus in the right place.
Does what it says on the tin. The focus point is in the middle, always. Sure, this could be useful if your dog’s eye is right in the middle, but even then you’re inviting the camera to focus on the nose, since it’s likely to be closer to the camera, shinier, and more centred than one or the other of the eyes.
Tracking / Lock On etc
Some cameras have other options, for example a “lock on” tracking option. These usually give the camera the entire scene to choose where to focus (remember what I said about giving the camera control?) and once it finds its subject, it will lock on and track them wherever they move. This might be useful for action photos, photos of puppies or dogs running around where you can’t physically move your camera enough to follow them… but I don’t recommend it for portraits as it’s not usually reliable enough to find the eye.
This uses a relatively large focus area which you can move around the screen. For some cameras this may be for example, 9 focus points all grouped, and the camera will attempt to find the subject/area of contrast to focus on within those 9 points.
I use this mostly for self portraits, as I know generally where I’ll be in the frame, but not exactly enough to be able to use a smaller focus area.
Searches the entire frame for what to focus on. Complete control is given to the camera. If it wants to focus on the ears, nose, background or a piece of grass in the foreground, it can.