Compiling
is the general term for taking source code written in one language and transforming into another.
Transpiling
is a specific term for taking source code written in one language and transforming into another language that has a similar level of abstraction.
Transpiling is the process of converting the typescript into javascript (using Traceur, a JS compiler).
Though typescript is used to write code in the Angular applications, the code is internally transpiled into javascript.