A compiler takes in one language and outputs some other language. E.g. C to LLVM IR or LLVM IR to x86_64 assembly.
An assembler is a type of compiler that takes in an assembly language and outputs machine code.
A transpiler is a type of compiler that takes in a language commonly used by humans to directly write programs and outputs another language commonly used by humans to directly write programs. E.g. c2rust is a C to unsafe Rust compiler, and since both are human-used languages it's a transpiler. Assembly language isn't commonly written by humans though it used to be, so arguably compilers to assembly language are no longer transpilers even though they used to be.
The existence of a transpiler implies a cispiler, a compiler that takes in code in one language and outputs code in that same language. Autoformatters are cispilers.
An assembler is a type of compiler that takes in an assembly language and outputs machine code.
A transpiler is a type of compiler that takes in a language commonly used by humans to directly write programs and outputs another language commonly used by humans to directly write programs. E.g. c2rust is a C to unsafe Rust compiler, and since both are human-used languages it's a transpiler. Assembly language isn't commonly written by humans though it used to be, so arguably compilers to assembly language are no longer transpilers even though they used to be.
The existence of a transpiler implies a cispiler, a compiler that takes in code in one language and outputs code in that same language. Autoformatters are cispilers.