Variations of Markdown with differing syntax are called "flavors." Markdown flavors are listed at https://github.com/jgm/CommonMark/wiki/Markdown-Flavors.
A Markdown flavor can be implemented in various programming languages and software applications. Libraries that implement a Markdown parser are listed at https://github.com/markdown/markdown.github.com/wiki/Implementations and https://www.w3.org/community/markdown/wiki/MarkdownImplementations.
Several Markdown flavors, and the differences between them, are documented at http://flavoredmarkdown.com.
To test and compare Markdown code in many different flavors, and implementations of those flavors, you can use the online tool Babelmark.