TextPad uses the term "Posix" to distinguish between two styles of syntax for regular expressions. See TextPad's help under How to... | Find and Replace Text | Use Regular Expressions.
The term "Posix" is a misnomer here: the Posix standard defines two syntax styles and semantics of regular expressions -- basic and extended. The setting in TextPad affects the syntax only; it doesn't affect the expressive power of TextPad's regular expressions (which is weak by current standards).
The syntax style that TextPad calls "Posix" tends to produce more readable regular expressions.