What is the difference between Coinbase exchange and Coinbase Wallet?

Could you please elaborate on the distinction between Coinbase exchange and Coinbase Wallet? As a cryptocurrency enthusiast, I'm eager to understand the key differences in terms of functionality, security features, and the overall user experience. Specifically, how do they differ in terms of storing, buying, selling, and managing digital assets? Additionally, what are the advantages and limitations of each platform, and how do they cater to different needs of crypto traders and investors?