Before reading this text you should know what’s the difference between Vector and Raster images. We posted already a simple explanation and if you missed it you can find it here!
Photoshop and Illustrator are two different programs that offer very different things. Photoshop is mainly for photo manipulation but you can also do some drawing on it but it is not as good as Illustrator. Illustrator is a vector based program which allows you to draw vector items. Vector is math based and will basically allow you more freedom if you are going to create something that will need to be various sizes since vector shapes are ‘math’ based you won’t have problems with things being pixelated when they are made larger. Most Graphic Artists use a combination of both programs.
Basically with photoshop you can create images like normal photos and with illustrator illustrations, logos and much more.