These tools can be accessed by clicking and holding on the current icon to see the submenu, or by cycling through them pressing the keyboard shortcut key W.
Both of these tools are similar in that they are used to select large areas of an image. The Magic Wand tries to pick everything it 'guesses' is the same colour as the area you click on within that one area. The Quick Selection Tool allows much more precise selections.
Let's start with the Magic Wand Tool to see exactly what it does.
Here we have a random stock image of rocks and sky:
Now if I try to select the blue sky in one go just by clicking on the blue, this is what I get:
Which is a pretty good effort, and wouldn't be too difficult to select the wispy clouds that were excluded. As with the Marquee Tools, to create multiple selections, just hold down the Shift key while you select. Now if I select something more complex like one of the rock faces, the difficulties here are that each rock face is made up of many different shades and colours. See what happens:
See the very grainy selection on the bottom right-hand rock? Let's zoom in and see it closer:
You can see that it has selected the same colour across three different rocks, but missed out other colour patches. Even though the colours are similar, the wand differentiates. So as you can see, the Magic Wand is good for big blocks of colour, but not detail.
Now let's look at the Quick Selection Tool.
I will start by selecting that same rock. The controls for using this tool are very simple. Click and drag in the shape/area that you want to select. Any further clicks will add areas automatically to your selection. If you want to refine your selection by removing parts of your selection, hold down the Alt key on your keyboard while you click. You will see that the cursor goes from having a small + sign to having a - sign. Using the tool this way will allow you to get an exact selection. See the video below as an example.
And the resulting selection looks like this:
The Quick Selection tool will also work well on block colours, but most selections generally have to be refined as it will follow contrasted edges more than colours for its selections. For instance if I choose the blue of the sky again, it will also select the sunlit rocks at the top of the pile.
So for block colours, use the wand, for more intricate selections use the Quick Selection Tool.