I don't know the level you are working at so I'll paraphrase/simplify for now -
FWIW CLB/CON switch inhibited below 400' AAL.
If pressed with 2 engines running changes engine thrust limit to the FMC selected climb thrust.
1 engine out increases thrust limit to MAX continuous.
(In reality if your SOPS involve using VNAV it's not a switch much used since VNAV should take care of the engine handling, even if an engine fails on takeoff, as long as the FMS is working properly).
OTOH the FMS VNAV "ENG OUT" function does a lot more than just control thrust or the indications thereof - it's interfacing with the likes of target speeds, makes info on engine out capability available to the crew, can be used to do a "automated" drift down...obviously the full details are in the FCOM.
Last edited by wiggy; 24th Apr 2017 at 16:54.