Clay will get contaminants that washing wont, The most popular reason to use it is to get the surface smooth when it gets rough and even after a wash the surface is still rough. This means you have embeded contamination and the only thing that will get it is claying or polishing. Claying is less aggresive so it's more desirable. Only polish if you have to, IE you have swirls or oxidarion and you want them gone. You can also use clay to get stuff like overspray and brake dust and plenty of other things that stick to paint.
Think of paint like a test and clay like an eraser, the only difference is that you need to keep the eraser and test lubricated with a lubricant or the paint will get swirled. But the motion you'd be using is like an eraser, many passes with medium pressure. Use a clay lube until you have used it alot than you can try other stuff like washes. Clay lube offers the most lubricity.
You can wash your car after, but it all depends on what you are doing. If you are going to wax, or not. I only use Zaino anymore so after claying I wipe the surface down with Z6 and then apply Zaino's Z5Pro and Z2pro. If you aren't waxing, it might be possible just to dry it depending on the lube. For more info check out detailersclub.com. Peace
