Fairy Tail (2014) left off when Igneel, Natsu's Dad, died and killed by Achnolgia. Natsu couldn't stop crying. Igneel's last words inspired Natsu and he left to go training with Happy. The rest, Gray, Juvia, Gajeel, Jet, Droy, Lily, Wendy, etc... left to go training too.
Fairy Tail Zero began when they all went to training. It was shown for about 2 months and it was all about Mavis and about her past. It also showed how Fairy Tail was made and the founders and how Mavis and the founders got magic.
After Fairy Tail Zero, A new arc began and Natsu has returned to the Grand Magic Games! There he met Lucy for the first time after a year! Things got pretty "hot" there. Fairy Tail is officially back and ready to go back on quests!