A blouson top is mostly a loose fitted top that may or may not cover the hips. It is not so tailored to a shirt, hence easily adaptable for various body types. Blouson can be various varieties and they were actually a replacement of shirts for women. Blouson is not very fitted by style, hence there is an ease to the wear unless you opt for the stylized version like a peplum blouson.
A shirt is a tailored top, with button opening at the front from collar to hem. Since it is tailored than a blouson, it has a restriction to wear for women with heavy bust/midriff variation. Shirts were traditionally part of men’s wardrobe, they started seeping into women’s wardrobe in 1950’s.
Both can be as formal or casual depending on the style, cut, color, finish, texture and print/pattern.
You can read about types of Shirts & Blousons and you can also read about formal to casual shirts plus formal to casual blousons.