Vector mask is mask which will be added to layer automaticaly when you work with shapes in Photoshop. There are two types of masks-layer masks and vector masks. Both control which parts of an image or layer will be hidden or revealed, and the masks can have special effects and styles applied to them. (See related link)
Both are Adobe products, Photoshop is pixel, raster or bitmap based editor, and Illustrator is vector based. In both programs you can work with pixel and vector images, the difference is in number of commands and possibilities in work with particular job. In Photoshop you have more possibilities to work with pixels and vice versa.
with corel draw you can output in all common formats
There are a few. Vector graphics are more "scalable" than raster graphics. By this, I mean you can draw a design that's six inches high, enlarge it to four feet high, and still have it look sharp. If you did that with a Photoshop file, the picture would become extremely jagged. Vector graphics' filesizes are smaller than raster graphics' filesizes. If I were to build a 12-inch square item at 60dpi, which is my standard resolution (you can get away with that if you're printing things that are to be viewed at a distance), and I did it in Photoshop, the file would be about 2MB. In Illustrator, it would be less than half that. I have a customer who gets pickups wrapped; I can do a whole pickup truck side in Illustrator in less than 20MB. That won't happen in Photoshop. Vector graphics tend to print faster than raster graphics do, and the prints are cleaner looking.
The different types of drawing software include professional software like CAD as well as vector and bitmap software. Some software includes 3D and technical drawing abilities. Most computers come with the free bitmap drawing program, Microsoft Paint.
There are several applications available to manipulate graphic images. If you are seeking to do touch up work or create digital images from photographic content best bet is Photoshop. However, if you are mainly wanting to "draw" line art type renderings Illustrator allows you to create vector images which you might use for clip art etc. The adobe suite is on of the most advanced packages on the market and is the standard for designers.
Vector masks are a useful tool for hiding the background of the image in certain type of images. Courtesy of: http://www.tutorio.com/tutorial/vector-mask Ps. There is also a tutorial as to how to use vector masks on this website.
Click on vector mask thumbnail if You are creating vector mask (fade as You say is visible when vector mask on LAYERS palette have border around), another way is to expand PATHS panel and click outside of path (have blue background color when is active) to deactivate (deselect) it.
There is no such option in Photoshop. If you mean Vector Photoshop shapes then the shapes can be used for infinite things in Photoshop such as layers, masks, as frames, as a source for selections, as a source for actual brushes, for patterns, for exporting to other applications, used in shape blurs, used as cookie cutters in Photoshop elements. Illustrator vector brushes exist as do expression and Xara vector brushes and many others but sadly, as yet, Photoshop has no vector format brushes.
Wrap option in Photoshop allow you to distort pixel based and vector objects. This option is mainly present in Photoshop for curvature distortions of pixels, text or vector shapes.
raster
Adobe illustrator (AI) is a vector file format to save vector illustrations. It is the default format for Adobe illustrator. Photoshop cannot save the images in to AI format but it can be opened in Photoshop.
Softening, you can soften edges of selection using Feather command from select > Modify > Feather or From Refine Edge dialog Select > Refine Edge. Feather also appears on Properties panel in Photoshop CS6 or Masks panel in previous versions to soften edges of pixel based or vector mask (you must select mask on Layers panel first).
Photoshop and Illustrator for vector.
Photoshop have Horizontal Type Tool and Horizontal Type Mask Tool which you can use to type text in Photoshop.
Mask will be saved as Alpha channel in CHANNELS panel (Window > Channels).
Photoshop can handle vector graphics, as can Illustrator.
Photoshop can handle vector graphics, as can Illustrator.