It's a newer model of the same old TIE Fighter.
To use a modern military comparison, the Super Hornet is an upgrade to the old F/A-18. Except it is such a drastically different aircraft it is almost always represented differently in military sims. The Tie/fo is the same way. Superficially similar but everything that actually runs the ship is different. So yes it is absolutely a new ship. Also given that apparently the First Order has a crush on the old Empire, visually emulating one of the most visible signs of their military might would be something they would do.
In game terms the things run completely differently from a Tie/ln. Also seriously a lot of the named pilots for it would not have worked in a regular Tie.
But they didn't have to. And they shouldn't have. Because it didn't deserve to be. Because it WASN'T a different ship.
In terms of the actual lore you're basically completely wrong. But really, how is it not a completely different ship, made in a completely different era, by a completely different manufacturer, to an obviously different set of design principles. The fact it even has shields makes it obvious that they are not nearly as throwaway as the old Ties were.
