The carriage return is moving the typehead to the beginning of the line, not starting a new one.

Line feed is the command that is incrementing to the new line.

Those two commands almost always run together so it quickly became possible to invoke with a single CRLF command (in ancient computer times)

I know, and the Return key both returns the carriage and feeds the paper forward a line on teletypes. Hence the symbol ⏎, indicating "down and to the left" (for LTR languages.)

The symbol is a bit awkward in conjunction with the name "Carriage Return" though, because the Carriage returns to the right. (assuming left-to-right writing)

You know I have literally never noticed that, but you're right. The carriage slides over to the right, leaving the levels to hit the left side of the paper.

Why it just shows what happens on the paper?