Compiling vs Transpiling
The definition you have quoted above is too general for a beginner to understand completely and so let me just simplify it to something we see practically.
Compiler: is an umbrella term to describe a program that takes source code written in one language and produce a (or many) output file in some other language. In practice we mostly use this term to describe a compiler such as gcc which takes in C code as input and produces a binary executable (machine code) as output.
Transpilers are also known as source-to-source compilers. So in essence they are a subset of compilers which take in a source code file and convert it to another source code file in some other language or a different version of the same language. The ouput is generally understandable by a human. This output still has to go through a compiler or interpreter to be able to run on the machine.
Some examples of transpilers:
Now, what do they mean by "similar level of abstraction": As I said it compiles/transpiles to a source file, one can argue that assembly language is also a source file and thus gcc is also a transpiler. So, this argument is what this similar level of abstraction voids.
The notion of categorizing languages into lower, middle and higher level is based on the level of abstraction they provide from the actual working of the machine/architecture.
So, a transpiler compiles to a language that is closer to the language you started with in the terms of this abstraction (or is closer to the level of that language in the lower-middle-higher level language ladder).
Hope this helps!
Here's a sort of descriptive way to answer
If you think of layers of abstraction as this example:
A compiler goes to a lower level (lower number). A transpiler switches from one language (or version of a language) to another at the same number.
I mostly agree with tapananand answer, but...
Words are "made", so they serve a purpose. And this also changes with time.
We now tend to use transpiler to specify a compiler that translates code into some other code "more similar" to the source one, that what a compiler might do. And is used to differentiate both mostly when both of them are mentioned in the same context (again mostly implying that a transpile language will have to get compiled at least once more)
So everything is very subjective. At the time of this writing:
- Coming from the Java world I could call CoffeeScript/TypeScript transpilers to depict that the resulting code is no more efficient than the original one.
- Babel calls itself a compiler.
So transpile is at this time very rarely used anymore, and only to tell two compilers apart.
It will probably dissapear as concept, since compilation is much more complicated than that (same/higher/lower language, version, etc), and the word doesn't seem to be useful anymore ("transpilers" are now ubiquitous)