No, you can play them in any order. If you pick Claude as your MC in the second game the opening cinematic kinda spoils what happens in the first game but other than that there’s nothing major really overlapping in the two games story-wise.

Second Story is the sequel to First Departure, taking place like 19 or 20 years after.

I guess this is why they never released Second Evolution R back when they did First Departure R. They had this in the works.