Techsmith is the company. It has two principal products, Camtasia (for producing videos, primarily, though it can produce stills as well) and Snagit (for producing stills which are screen captures primarily, though it can produce videos as well). Both can output in standard formats like .mp4 for videos or .jpg or .png for stills, and those can be used as components of a web site.
If you mean for mocking up a web site page, though then the answer is still yes, but Photoshop is more powerful in terms of creating elements and can integrate with Dreamweaver. It's a steep learning curve though.