[1][2] Both are used together in a computed form of error detection to ensure that data received at the remote destination of a telecommunication are the same as data sent from the local source (a/k/a echoplex, echo check, or loop check).
Typically 'local echo' accompanies half-duplex transmission, which effectively doubles channel bandwidth by not repeating (echoing) data back from its destination (remote), as is reserved-for with 'full duplex' (which has only half of the bandwidth of 'half duplex').
[11] Whereas the Network Virtual Terminal that the TELNET protocol itself incorporates is a half-duplex device with (by default) local echo.
Others include modems, some form of intervening communications processor, or even the host system itself.
[8] For several common computer operating systems, it is the host system itself that performs the echoing, if appropriate (which it isn't for, say, entry of a user password when a terminal first connects and a user is prompted to log in).