Is Crash 4 a remake of Wrath of Cortex?

No, Crash 4: It's About Time is not a remake of Crash Bandicoot: The Wrath of Cortex. Crash 4 is a brand new installment in the Crash Bandicoot series developed by Toys for Bob and published by Activision. It continues the story from Crash Bandicoot: Warped and introduces new gameplay mechanics, levels, and characters. While both games feature Crash Bandicoot as the protagonist, they are separate titles with distinct gameplay experiences.

Crash Bandicoot 4: It's About Time (get it?) is a direct sequel to that PlayStation 1 trilogy, forgoing The Wrath of Cortex and all of the other main-series games since then. There are a few reasons for that.