I believe the application you are talking about is Grab, with the logo as a background of a window with scissors in front. The purpose of the application is take pictures of your screen. For example, if there was a cool picture you saw and couldn't download, you could use Grab and highlight the picture and it would be saved as a picture.
This is for Max OS X.
An icon is a logo for a program
Icon
You may be referring to a path or shortcut icon on the desktop that points to a specific file or program.
Icon
An icon.
The word you are looking for is icon.
pinned
A symbol on your desktop that is a shortcut to a program, such as Microsoft word.
A group icon contains program icons. For example, the Games group icon contains several games.
VLC player
Icon.
shortcut