Photoshop is raster based but you can work with vector objects in Photoshop. Why is raster based is question for founder Mr. Thomas Knoll not for public because we can not answer this question. Maybe because this world need raster based software.
raster
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Photoshop is a raster image editor. Raster and Bitmap are two words for the same thing, so Photoshop is raster or Bitmap image editor, somewhere you will see raster, somewhere bitmap as explanation but it is basically same thing. Photoshop is primarily designed to work with bitmap images which are raster images in other words.
It is question for Photoshop and Illustrator developers, which tool is from which app but Illustrator have Photoshop raster filters, that's for sure.
Many famous image manipulation / graphics editing software programs are raster based, including: Paint.net, a lightweight editor featuring far more options than the unrelated MS paint, the GIMP, an open source equivalent to photoshop designed more for advanced users, and the ever-famous Adobe Photoshop, a long time staple of graphics editors everywhere.
Yes, Photoshop is software itself.
Raster or Bitmap image.
You can open an eps file in either Photoshop or Illustrator, it helps to know if it is raster (use Photoshop) or vector (use Illustrator).
what is photoshop?
Some editors specialize in the editing of (digital) photographs such as the popular Adobe Photoshop or RawTherapee, while others are more geared to artist-created illustrations, like the Adobe Fireworks. Usually an image viewer is preferred over a raster graphics editor for viewing images.
Photoshop is a raster/pixel-based program, and is also a product you have to purchase. Inkscape is a vector drawing program that's free.
Photoshop is software, most popular in image editing.