A PSD file is known as a Photoshop document and was developed by Adobe in order for Graphic Designers to create layered images. PSD is the propiertry format that Adobe uses to allow these files to be saved in, they can then be either opened in various versions of Adobe Photoshop or if a user wants to send them to others they can be flattened to PNG, JPG or other more standard image formats. You can't however re-convert a JPG/PNG file that has been converted from a PSD back to a PSD file - it loses it's layers.
Photoshop files have the .PSD file extension, this PSD stores an image with support for a lot of imaging options such as Masks, transparency, clipping paths and duotone settings. Sometimes Photoshop files have the extension .PSB which essentially stands for Photoshop Big, this allows images to support up to a maximum height and width of 300,000 pixels and a length limit of 4 Exabytes.
PDF is a file format developed by Adobe Systems for representing documents in a manner that is separate from the original operating system, application or hardware from where it was originally created. A PDF file can be any length, contain any number of fonts and images and is designed to enable the creation and transfer of printer-ready output.
Each PDF file encapsulates a complete description of a 2D document (and, with the advent of Acrobat 3D, embedded 3D documents) that includes the text, fonts, images and 2D vector graphics that compose the document. They do not encode information that is specific to the application software, hardware, or operating system used to create or view the document.