letsencrypt renew is what you would run if you have installed the client through your package manager on a distribution that shipped an older version of the client where it was still called
letsencrypt, such as Ubuntu 16.04. The version in Ubuntu 16.04 is a bit dated and I would recommend sticking with
certbot-auto (which would give you the latest release).
Basically, if you’ve been using
certbot-auto, that’s what you should continue using. If you ever switch to a version of the client provided by your distribution’s package manger (as more and more distributions add native packages), the command would likely be
certbot going forward, but it’s perfectly fine to stick with the
certbot-auto installation method.