The equivalent of a Windows .exe file is called .app (for "application") under Mac OS X, although file extensions aren't always displayed. An .app file is actually a packaged collection of files, containing the run-time code and various resource files, but you don't have to be aware of that since Mac OS X makes it look like a single application file unless you specifically ask to see the contents.
Years ago, Mac files included within them a "creator" tag that identified what application they belonged to, so Mac OS knew what program to launch from the file's content, not the filename. But Mac OS X now relies by default on knowing what application to launch based on a file's extension, as Windows does.
Extensions such as .txt (text), .pdf (Acrobat file), and .doc and .xls (MS Office) are the same as Windows. Extensions for the main types of executable files are different. In addition to .app for executable applications, for example, there are executable .scpt files (one of the ways to store AppleScript files), and executable .command files (Unix-style shell scripts). There is also .workflow, an executable script created with the Mac OS X "Automator" application. Some executables, such as perl programs, can use the same extensions as under other operating systems.