What's the difference between a crypto wallet and an exchange?

Can you clarify the fundamental differences between a cryptocurrency wallet and a cryptocurrency exchange? Specifically, how do they differ in terms of their functionalities, security measures, and user interactions? Is it possible to store, trade, and manage cryptocurrencies through both platforms, or do they each serve a unique purpose within the digital asset ecosystem? Additionally, are there any specific benefits or drawbacks associated with utilizing one over the other?