There is only a single Rod in Sun/Moon. The fishing mechanics were substantially reworked. You no longer fish just in the water, you have to be near an underwater rock pile. If there are bubbles coming from the rock pile, then rare Pokemon have a higher chance of being caught on the hook. Personally it's a step backwards, but it's what we have.
You receive the Fishing Rod from Lana after completing her Trial in Brooklet Hill on Akala Island.