Well both are not written specifically because or for the web. They are image editing programs not web design programs. So in context of using the images after you have edited them in PixelMator or Photoshop, that you can use those images in your web page.
So I guess the short answer is yes and no, or just yes.
Adobe Photoshop is the most widely used professional image editing program in the industry, and it's used by professional photographers, web designers, and just about any professional who has anything to do with digitally editing images. Besides Photoshop, Adobe has a suite of other software, some of which is specifically for web designers (Illustrator, InDesign, Dreamweaver). See Adobe's website.
(Wow, that sounded like a commercial for Adobe...).
Web designers could draw stuff for websites in Photoshop, using layers, and export it all to Flash, so that a Flash website can be made with it.
PixelMator is an image editing program like Photoshop, ofcourse you can use it to edit images for websites, but it's not really meant as a complete solution for creating websites.
If you're looking for an image editor on the Mac, then Seashore is also a nice, and free, program you could have a look at. (It's not as sophisticated as Photoshop or PixelMator, but it's good enough for many tasks and it's free, unlike the other two).
John Todd wrote:AFAIK, Photoshop is used by web designers to design web sites (I'm not sure about the process but I know they export their designs to HTML).
Most of the people that I know use Photoshop to work on their images, and none of them create web sites. My Brother In Law does underwater photography and use it to fix the pictures up to remove air bubbles and stuff, so I never considered using Photoshop to design a website, and that Photoshop was around before Web stuff really started.