They're both FF titles. That's about it.
The only games with any sort of acknowledged connection are: FF Tactics and FFXII (both in Ivalice with many centuries difference), and FFVII and FFX (possible retconned tenuous connection that Spira becomes Gaia and Shinra the kid from X is the founder of Shinra Corp.)
Everything else is officially a distinct world.
As for the Magitek, they brought it back for XIV because it's a fun concept.