These two terms are not interchangeable for the simple fact that not all pink wine is sweet.
Blush refers to the sweet stuff, such as White Zinfandel, White Merlot, and so on. These wines have notes of strawberry and cherry, and LOTS of added sugar.
Rosé is a dry to semi-dry wine, with flavors reminiscent of its red wine counterpart. The fruit flavors most prominent are typically strawberry, cherry, and raspberry with some citrus and watermelon. In France, Rosés account for the vast majority of its wine production, with Grenache as the dominant grape followed by Syrah, Cinsault, Mourvèdre, and Cabernet Sauvignon.
Rosé is the ultimate summer and spring wine. They are typically inexpensive and are light, flavorful, and refreshing.