Open Office of which ODT is part of was developed by Sun Microsystems around twenty years ago. The software is open source and is seen as a viable free alternative to Microsoft's Office suite of products. Open Office opens most Microsoft document formats and is is provided as a free download, without restrictions on license. The writer application which produces ODT files is the word processing element of Open Office.
The Open Document Format is an open standard developed by Sun Microsystems under the guidance of OASIS (The Organization for the Advancement of Structured Information Standards). Originally the OpenDocument format was XML based and had at it's root, it now takes the form of a zip file much like Microsoft's DOCX format and takes advantage of the ZIP's compression technology to reduce the overall file size. Writer documents take the form of .odt and .fodt.
Microsoft Office 2007 Microsoft Office 2010 OpenOffice Writer
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.