This is true. Ignoring the labels, macros, and directives, there are many ways in machine code to encode most common x86 instructions (zeroing a register even has many possible assembly instructions!). Assemblers pick the best encoding.
Is that true? They swap actual instruction mnemonics as written in the assembly source into different instructions, for performance? I hope that is controlled by some flag or something, seems like a strange thing for an assembler to be doing unless asked.
I seem to remember the venerable combined assembler/monitor/editor ASM-One [1] on the Amiga having a mode to do that, an "optimizing assembler", but I think it mainly worked with instruction and data sizes, i.e. optimizing short jumps into branches which were cheaper on the 68k.
I believe that there are some assemblers that will swap "mov rax, 0" for "xor eax, eax" (which is smaller and faster), if you let them, but not all of them. Some instructions like "jmp LABEL" correspond to many different options (short relative jumps, long relative jumps, absolute jumps, etc.) and the assembler picks the best one.
As another example, almost all of the vector instructions have an encoding with a VEX prefix (an AVX encoding) as well as the older SSE encoding. If you mix the VEX and SSE encoded instructions, there can be a big slowdown, so an assembler will give you VEX encodings if you have AVX-only instructions in the stream, and default to SSE encodings if you don't (they are often smaller).
Some instructions, like LEAs and ADDs, have several different encoding options corresponding to different operand orderings, and an assembler will pick the best one - some of these encodings will force an extra SIB byte when you use R12 as an operand, for example.
This is kind of assembler-specific in terms of how smart it is. I'm not sure that the dumber assemblers do this for you.
