Not quite. The games have no direct story connections, but there are recurring themes, concepts, character and location names, and design elements that show up between different games, as well as occasional cameo appearances, like KOS-MOS and T-ELOS (Xenosaga characters) in Xenoblade Chronicles 2. All of these games have the "Xeno" prefix because they are all meant to be part of a wider franchise despite telling different stories and being produced by different developers, and series creator Tetsuya Takahashi has been involved in every Xeno game as a director and/or scenario writer.

Pretty sure Xenogears and Xenosaga are entirely different series, stuff that's not even Nintendo Property.