A markup language is a language which is used to represent structured data. For example, HTML enables to specify that some part of the document is a title or some other part is a list, by comparison to a flat text document.
Markup languages are not considered as programming languages¹.
The difference with programming languages is not always obvious. For example, XSLT is a Turing-complete language², but is based on XML which is a markup language.
Wikipedia itself makes important efforts to avoid qualifying XSLT as either a programming language or a markup language. It only says it's a declarative language, and that it uses “optimization techniques found in functional programming languages and database query languages”.
A scripting language is a programming language which is interpreted, rather than compiled, which means that scripting languages represent a subset of all programming languages.
It is not always obvious whether a programming language is a scripting language, like it's not always obvious whether a language is compiled or interpreted. For example, PHP may be compiled to intermediate bytecode³ and then ranslated into machine code by JIT compiler, while being still considered as scripting language⁴.
See also: Splitting Meta-Hairs by Steven Lott.
¹ “XML is not a programming language”. See XML in 10 pointsXML in 10 points.
² “XSLT is a Turing-complete language” See XSLT on Wikipedia
³ “HHVM compiles Hack and PHP into an intermediate bytecode. This bytecode is then translated into x64 machine code dynamically at runtime by a just-in-time (JIT) compiler.” See HHVM.
⁴ Scripting languages in List of programming languages by type on Wikipedia.
