Both the softwares are produced by the same company i.e. Adobe. Both these software have their own purpose like Photoshop works well in photo editing while Illustrator works well while making cartoon illustrations. Illustrator is a vector based graphics program that is generally used for illustrations and logo designs. It is used to create images that are small in file size, but can be resized to any dimension while still maintaining print quality.
Adobe Photoshop CS5 is the 12th major release of Adobe Photoshop. Photoshop is intended for use with raster images, if your drawing needs are small, Photoshop will probably work just as well. Bitmapped graphics are measured by the number of dots per unit - usually called dpi (dots per inch).Photoshop is often used to resize or crop images. Photoshop is also often used to create graphics for website layouts, such as banners or navigation buttons.

If you are only creating a logo for your web site and will never do any type of print, then Photoshop works great but if you are planning to create a logo and print it afterwards then Illustrator will work well. Whether it’s a Web designer, Graphic designer, Animator or a post production Artist both the softwares must be known to them,
Though there are a number of institutes giving training for these softwares but At ADMEC we develop and educate our students in such a way that it grooms them into the perfect & successful professionals.